Unless you are doing full grain or partial mash brewing, temperature really isn't a worry.
The kits are made to work within a range and for your house to be out of that range is unusual. I brew a lot (both from kits, partial mash and experimentation) all year round and I've never worried about temperature. It is not uncommon to be able to see your breath in my flat.
Edworts Apfelwein is the easiest and cheapest to start with. You can make pints of 8.5+% cider, which is tasty (after sufficient ageing, you're looking at 6 weeks in the bottle), for 30p a pint.
There's no reason to go out and spend anything more than £30 setting yourself up.
The biggest outlay will be bottles but chances are, especially if you are a student, you can get them for free or at the very least awfully cheap.
Second to that would be the fermentation vessel. I use 5 gallon plastic drums used for carrying liquids. There is
NO reason to go out and buy 5 gallon glass demijohns at this point.
Then you need a syphon tube and tap (a few quid off the internet, nothing more than a fiver)
A large funnel will save you a lot of time and hassle (again, about £2).
A hydrometer, get a glass one. About £5.
An airlock is pretty important, some people say you can use a balloon but I wouldn't. Though, again this'll only set you back £2-£5.
Santizing powder (you can use diluted bleach, but best to get some proper stuff. I recommend VMP, about £5 for a big pot.
You are then good to go.
Again, google Edworts Apfelwein and you'll be fine.
If you spend anything close to £100, you're a mug - unless you're going straight into full mash brewing which is daft at this point. Try some kits and see if you enjoy it.
As for time, you want to leave it for at least 4 weeks in the fermentation vessel. Then transfer it to bottles and you want to leave it at least a week in here for secondary fermentation (to make it fizzy). Though I would leave it for at least a month.
I have a couple of batches coming up to a year of ageing and shall be drank in August. They'll be 'gorge'.
This is my local brew shop -
http://www.innhousebrewery.co.uk/.
Most important thing is to make sure everything is sanitized and the air lock on the fermentation vessel and bottles is air tight.