Which category of Schengen Visa?

There are no strictly defined “categories” of Schengen visa and you can also always select “other”. It's true that there are some differences in the supporting documentation expected by some consulates depending on the box you check on the form but there is nothing stopping you from including more. The most important thing is to present a coherent story with a credible plan and all relevant information to avoid creating the impression that you are deceptive.

Specifically, having no income tax returns could be a problem in your case. It's sometimes possible to omit them if you are visiting close family, when you can credibly claim that your host will cover the costs of your stay and you have a proper invitation (one that's stamped/validated by the local authorities). But that's apparently not your case so you can't simply claim to be visiting a friend and rely on that to meet the financial means requirement.

Furthermore, documentary evidence of a stable situation are also useful to meet other requirements, which is another reason to provide tax returns even if you check “visit to family and friends” as the purpose of the trip. As @phoog explained, if income tax returns do not show you in a favorable light or you have none at all, you can also provide other things that show you have enough income and reasons to come back to your country of residence.

Since you are "visiting" a friend who is also a tourist (perhaps it's better to say you are meeting or traveling with a friend), you should apply as a tourist.

If you have been employed for only four months, and have no income tax returns, you can still apply. Just include a letter explaining that you've been employed for this short time and that's why you don't yet have returns. Show your pay records for the four months instead.

You will probably receive extra scrutiny as an overstay risk, because of the short term of your employment. Any objective evidence of your intention to keep your current job and return to your home will help (a lease for your apartment, for example).

My advise is to apply for a shot stay visa. this visa will allow you to travel for a maximum of 90 days in every 6 months period. with regards to your income tax, do you have other source of proof of income in form of your payslips and bank statements? if your payslip has details of your PAYE tax then you should be fine as long as there is some substantial amount in your bank statement to cover your trip.