Try to get a good deal on Ebay or a carboot or try Pets At Home.
3-5g is the best for bettas. The reason being it is unfair on the fish in many ways. The water params can not be kept stable for heat, also waste produce by the fish will build up much faster. The more important aspect would be that your fish should have the best home possible, a small container like that would be like you having to live in your closet, your able to move but it isn't good to live in.
I am sure you will find some great deals around, the bigger tank the better you and your betta can enjoy each other
So say £15 tank including filter, £8 heater, 99p sand, £5 betta, £5 decorations bare, £3 food = £31.99 say around £35 to set up with everything.
Once initial set up is done then it would just be food and oh! do NOT forget dechlorinater which is about £2 for a small bottle.
If you are lucky you may win a set up for tank, heater, filter, and some gravel for £10 and under. It is also better as well that you cycle the tank before introducing fish