Why was I refused 'Leave to Enter' at an airport in the UK (and subsequently removed)?

I'm worried about whether I qualify as being removed or deported

You were "removed", not "deported". To get very technical about it, you were issued 'administrative removal' under Paragraph 320 of the Immigration Rules because you failed to qualify as a visitor under Appendix V of the same rules.

and if there is an ensuing ban in place.

There is no ban in place. Were there a ban they would have served you different paperwork and you would be aware of it. They don't ban someone during a portside removal anyway (except in the most egregious cases like forgery, identity theft, contraband and the like).

Can you offer any insight? Does this count as deportation, or simply a matter of course during the refusal of leave to enter?

Assuming that your visit was to maintain a relationship with your 'sponsor', then the latter would apply. It's fairly normal for people pursuing long distance relationships to try and conceal this during their landing interview or to have discrepancies in their story. They do not consider that sort of thing to be the type of deception that attracts a ban, but Immigration Officers get very annoyed when they are being lied to.

You will need to report your removal when you apply for entry clearance.

Your removal notice has your 'Port Reference' number on the top, don't lose it. You will need to provide this when you apply (or optionally add several weeks to your waiting time).

Secondly, how much money is necessary to have evidence of for a one month visa?

There is no prescribed amount but it should properly agree with the purpose of your visit. If you are planning to cohabit with your 'sponsor' then you wouldn't need a lot for maintenance and accommodation.

Can you offer any insight?

You wrote that you are applying for entry clearance, this is recommended (but not required) following any sort of removal or refusal. The big problem I see in your narrative will be establishing that you are a genuine visitor. Most visitors plan to stay for about 2 or 3 weeks because they have jobs and other commitments to attend to, and part of your challenge will be to prove that you have those types of commitments. It's safe to assume that you do not because your landing interview would have turned out quite differently were you able to present a coherent picture of a bona-fide visitor to the Immigration Officer. Also, showing up in the UK without a return ticket is pretty much an open admission that you do not have strong ties to your home country, and that's something they will look for.

I am now attempting to make a visitor's visa to return to the UK

That is the recommended strategy for your situation. To apply you would create an account at Visa4UK and fill out the form. A UK Standard Visitor Visa (which is formally and technically called 'entry clearance') will reduce the problems of arriving in the UK and your landing interview will be more of a formality. The first page should be filled out like this screen shot...

For the purpose of your visit, you can explain that you are maintaining a long distance relationship and include a statement from your 'sponsor'. It is also emphatically recommended to wait before hitting 'submit' until your circumstances are stable and your homeland ties are plainly evident. If these are not in order, your application will be refused and then matters will be worse...

Any suggestions for what to include as far as evidence when I make my visa application?

At this point you can plan to spend some time carefully studying the guidance along with Appendix V of the Rules. The guidance will help identify what evidence they will be looking for.

Note: The question about 'deportation' versus 'removal' is here.

Note: Related question with redacted removal notice on Expats.

Note: A similar question (but not a duplicate) in the TSE archives is here.

Note: Per the comment by phoog (to whom thanks), having a proper visa (entry clearance) in your passport before you leave your home country is different from getting 'leave to enter' when you arrive in port. Both of these options are available for Americans, Canadians, Aussies, and so on. I will concede that the UK is in a totally different orbit with respect to visas and terminology. Sadly, if you are going to conduct an LDR, you should familiarize yourself with it.

The answer by user Gayot Fow covers most of your questions asked. As you appear to have only gotten in to this situation by seemingly badly misunderstanding the requirements and processes for entering the UK as a presumably visa-exempt (I will assume US) citizen, I will try to explain how the systems actually work. Most of the problems described here appear to have derived from trying to tell the Immigration Officer what you thought they wanted to hear, rather than just what you intended to do.

The UK does not, except in a very small number of exceptional circumstances, issue visas on arrival at a UK border. To even be allowed to board a flight, a visitor should either be in possession of a avalid visa, or holding a nationality that means a visa is not required. British and other EU citizens can come and go pretty much however they like. For other "non-visa nationals", leave to enter can be granted at the border by an Immigration Officer(IO) according to section 23A of the immigration rules. To find out if you are a visa national or not, you can use this tool on the UK government site.

The leave to enter can be granted for up to six months (and in most cases, will be), even though most visitors are anticipated to leave much sooner than that. In your particular case, you seem to have caused considerable confusion by requesting a 3 month visa when a)no visas are available at the UK border and b)you intended to say for much less time than that. What the IO actually wished to know was how long you intended to stay.

The three month time period the IO understood you as intending to stay caused the IO several aspects of concern - they were unconvinced that you had the resources to support yourself, and you were unable to provide evidence that you could support yourself for that long (no, most people don't travel with bank statements, but sometimes these questions do come up). This raises several concerns:

1. that you may undertake paid work to support yourself while in the UK
2. That you will be unable to support yourself, and may end up without proper accomodation (espeically given that your sponsor only indicated expecting to host you for 1 month) or seeking help from the UK government
3. That given the lack of a return ticket in advance, you would be unable to afford one and to leave before the end of your leave to enter.

The disagreement between yourself and your sponsor as to the nature of your relationship again undermines your credibility. While visiting a romantic partner may lead to extra questioning, it is not a reason on its own to refuse entry (entry is only refused when the IO beleives that the visitor may be seeking to remain and form a life with the romatnic partner and reside in the country illegally - something which, unfortunatley, your lack of a return ticket would have made look more plausible). However as you claimed there was not a romantic relationship with your sponsor, while they claimed there was, this causes the IO to wonder if other things you have told them are bending the truth somewhat.

In principle the IO when considering giving leave to enter is considering if you will: 1. Leave on time; 2. Follow the rules for visitors when in the country. You can find a full listing of the rules for visitors here, in Appendix 3 of appendix V of the visitor rules, but they are well summarized on the advice page about visitor visas:

You can:

• take part in any of the business-related activities mentioned in the Visitor Rules
• study for up to 30 days, as long as it’s not the main reason for your visit
• take part in an exchange programme or educational visit (if you’re under 18)
• convert your civil partnership into a marriage

You can’t:

• do paid or unpaid work
• live in the UK for long periods of time through frequent visits
• get public funds
• marry or register a civil partnership, or give notice of marriage or civil partnership

In future, while you do not technically need a visa to the UK (again, assuming US citizen), the fact that you have been refused before is likley to make you be subject to closer examination again. Getting a visitor visa in advance is the recommended course of action now.

As this situation appears to have come about through a misunderstading of the requirements and rules of a foreign country, I would like to direct you to a section of the website of your (again, assuming US citizen) State Department, where they explain the entry requirements for US citizens to various countries around the world. Understanding this will hopefully avoid similar problems on visits to other countries (although in the even of a conflict between State Department advice and that of the national you are visiting, you should listen to the destination country's version of its own rules)