Do I have to register as a business with Companies House (I'm in the UK), or is it optional?
You have two choices, either incorporate as a private limited company, or trade as a sole trader. A PLC is a little more complex admin-wise, but it makes a clearly separation between company money and your money and limits your liability in the case of financial problems. Only the PLC needs to be registered at companies house.
The effective tax rate is generally slightly lower for a PLC if you're able to pay yourself in dividends. But if this is a one man band business combined with a full time job I think acting as a sole trader and an employee is very difficult accounting wise. Forming a full PLC is also excessive overhead, so my suggestion is to find a friend who owns a company and ask if you can trade through their business account and be paid as an employee. Obviously, they'll need to be a good friend.
Do I have to have a business bank account?
No, but it's generally unwise to operate commercially without a business account. If you got audited by HMRC, putting them together would make your life very hard. It would also make bookkeeping very hard.
In terms of book keeping, if your revenues justify it, I'd recommend FreeAgent very highly. It's online book keeping software for sole traders and PLCs. My accountant reduces his price by more than the subscription cost because it present the accounts so well for him to analysis. But don't add any expenses if you don't have much revenues, obviously.
Lets say I rent a server in another country (lets say Slovakia) where
I will be hosting my mail server, do I need to register as a business
I'm not taking a profit from my business as I work full time, if this
project made any money it would be re invested back in the business,
so presumably I don't need to register as self employed?
Your profits, income, whatever, don't technically have any bearing on the form of the company. If you're saying you don't intend to take a salary ever, apart from the question of the point of it, there are still reasons to incorporate. One is the problem that a business account is generally a better idea and two is the fact that you are still liable for your actions. If you do this as an individual and cause another company to lose money, which they decide to sue you for (unlikely, but possible), you'd realise the advantages of a PLC at that point.
Running a business overall isn't really something to "play" around with. You kinda need to either do it properly or not at all.
If it's a case of 200 quid a year, then HMRC would be unlikely to press you for format accounts, you could probably get away with just paying it to yourself and declaring it on your self-assessment (if you don't already do that, you'll have to start). I could say contact an accountant, but given that'll probably cost more than your earn, I know it's unlikely you will :).