Is an Oyster card worth it for 3 days?

If you really, really want to save every pound, then if you get an Oystercard (or have a contactless debit or credit card) and use only buses to get from Heathrow to Balham (you can do it in three bus journeys, taking a bit over two hours in total) you will be charged £4.40, the daily cap on bus fares.

In general, if you want the cheapest way to get around London, you should stick to buses (and the Croydon tram) and not use the Underground or other rail services. Buses are slower, but they're cheaper and they go everywhere.

To get from Heathrow to Belham, you can take the bus to Victoria Station for £5.70 cash. Comparatively, you can take the train from Heathrow to Paddington for £21.00. People wanting to save time will take the train, which is about 15 - 20 minutes; the bus takes a lot longer. It's a close call between the two because you'll be fatigued and lagged after a lengthy flight and clearing UK immigration.

For your larger question, you would be advised to get a Visitor Oyster Card for a one-time fee of £3.00. You top up the card as you go; the lowest amount to add is £10.00. They recommend getting a Visitor Oyster Card pre-loaded with £15.00, which should last you about 2 or 3 days if most of your travel will be in Zone 1.

Oyster Visitor Cards have a daily price cap on how much you will pay. The cap varies depending upon whether you travel at peak times or off-peak times. For example, if you travel during off-peak, the cap is £8.40, even if you take 20 trips. The price cap is also a feature on standard oyster cards.

You can always get a refund of the unused balance by taking the card to a tube station or sending it to them. They refund the balance in cash and return you the card with a zero balance.

You can order a card on-line and have it sent to you, it takes 8 to 14 days for an international order to arrive by post. Transport by Oyster is slightly cheaper and you will recover the £3.00 one-time fee in about 3 days of usage. Plus you can use it in future visits because Oyster cards never expire.

To order on-line, visit http://visitorshop.tfl.gov.uk/oystercard/product/oyster-card.html

If you totally want to maximise your budget then then the absolutely cheapest way is to walk.

Heathrow to Balham, for example, is 15 miles - google maps says a bit under 5 hours, obviously it depends how fast you walk.

Balham to Westminster is much shorter, of course.

The advantage (apart from it being free) would be that you'd get a real feeling for the genuine character of the city.

The disadvantage would be that you'd spend quite a lot of time walking through suburbs that aren't usually considered tourist attractions (but that actually show the contemporary life of the city more accurately than the Tower of London or the British Museum).

London as a city is extremely friendly to pedestrians - plan your route from heathrow avoiding the A4/M4 (big highways) and it could be quite an interesting little urban hike.

Is an Oyster card the most cost-effective way, or buying paper tickets?

Yes, it's worth it, in strictly financial terms. You always (or very nearly always anyway) get a (slightly) cheaper ticket price with the Oyster card than you do with paper tickets, and when your journey is over, you can turn in your Oyster card and receive a cash rebate for any unused credit plus the original £5 deposit for the card itself.

So strictly speaking, even for a single journey, the Oyster card is cheaper (although more of a hassle, so maybe not worth it in an absolute sense, depending on how you value your time in relation to your money).

Short answer

Use your existing contactless bank card, don't buy an Oyster Card.

Reasons

1. You can skip queuing for a few seconds at a ticket machine to buy an Oyster card
2. You can skip queuing for a few minutes at a ticket office, after your holiday, to get your £5 Oyster deposit back - quite a few people forget this step and end up with the Oyster card permanently taking up some space in the wallet
3. A contactless bank card uses the same fare algorithm as an Oyster PayG, and is cheaper than Oyster PayG if you stay from Monday to Sunday
4. If it is an international bank card, you would have paid the same makes-no-difference currency coversion charges to buy an Oyster card
5. You rather skip the Oyster and thus have one less card in your wallet during your stay

More tips

The bus service from Heathrow to Victoria is actually a National Express Coach service. This doesn't add to the daily capping. It is far cheaper to take the bus + National Rail than a Coach.

1. Red - Bus 285 from Heathrow to Feltham station
2. White - Southwest Trains from Feltham station to Clapham Junction
3. Dark Green - Southern Trains from Clapham Junction to Balham

I recommend to use public transport rather than walk stupendously long distances. Chances are, you might eventually use public transport that day and quickly hit the fare cap. That would render the money-saving long walk as pointless.

To pay the least fares, remember to touch-in and touch-out when using trains, even when the ticket barriers are open or when ticket barriers don't exist.

Also, regarding "Visitor" version of the Oyster cards: I feel this is pointless, even before the days of contactless. I wouldn't purchase this for a non-refundable £3 card before travelling to London. What if the holiday is cancelled? Moreover, it's not like there's a dearth of vending machines to buy a normal Oyster for a easily refundable £5. That said, as a commuter using the plain blue Oyster, I wouldn't mind getting a Visitor Oyster as a collectable.