Hello and welcome! It's always great to see someone who does lots of research before buying!
The aquarium size you need depends on maintenance schedules, budget and what you
prefer. Pets At Home sell 21 (5 gallons) to 26 (roughly 6 gallons) litre aquariums for around £20, they include a filter (which is unfortunately too powerful for a betta), some other bits and pieces and can be safely cycled. You can also buy themed tank sets from there (which may be better suited for your little one, though that depends on both your tastes
) that can
include some ornaments if I remember rightly.
If you want to cycle your tank you'll need a filter, I suggest sponge filters because they don't create a current unless you have the air pump needed to power them allowing a lot of air flow. Air pumps, sponge filters, air tubing and relevant valves (control valve (usually included with the pump) and non-return valve) can add up in price but if you shop around and take a peek online you'll be sure to find a good deal. Sponge filters release a steady stream of bubbles that can be increased or decreased depending on your preferences as well as the fish's preferences (my betta, Echo, flares at the bubbles as they come out of the filter, it's rather silly
If you think you'll want to add tankmates at a later date (this depends on your fish's personality as much as anything else) please make sure you consider this when purchasing an aquarium unless you're willing to upgrade later if needed. As this is your first betta (and pet animal -- welcome to the world of pets
) I'd suggest sticking solely to him/her, they are very hardy but many suitable tank mates will not be so forgiving should any beginner mistakes be made.
Once the fish's initial set up is taken care of the rest isn't at all difficult. Regular water changes (twice weekly for tanks under 20 litres (5 gallons): one 50% and another 100%, one weekly water change for cycled tanks above 20 litres), warm water (a heater is a must, adjustable ones are ideal!) and good food & water conditioner and you're set.
It may also be worth checking out Wilkinsons and Argos as well, both have own-brand tanks (Argos' is rather expensive but they do seem to have regular sales) that may be better value than named-brand ones found at Pets at Home (though Pets at Home also have own-brand tanks and kits). The only issue I have with Wilko is that they advertise most of their small tanks for goldfish (which is bad as the tanks are tiny compared to what goldfish actually need). You might even find a good quality, second hand aquarium at charity shops or on eBay, depending on if you prefer to view items in person before buying or not. I would
suggest getting a name-brand heater, thermometer and filter though as they are usually more reliable in my experience. Good brands (again, in my opinion) are Elite and Interpet.
Bettas make a wonderful first pet and are often very interactive once they adjust to their new home. If you have any independant aquarium stores locally it might be worth stopping into those to see if they stock bettas, they're usually much higher quality and there is a lot more variety -- generally they are costlier than those available from Pets at Home and other such chain stores but I honestly believe the extra money is worth it to ensure that you have a happy and healthy new friend.