1GB of RAM will probably do for the time being - I advise you to get 1GB sticks of RAM whether or not you install 1GB or 2GB
Depends -- using 2x512MB will give you a speedboost over 1x1GB, since the former can run in dual mode, where it spreads out the bytes across two sticks and can theorethically read/write data twice as fast.
Especially if you have a motherboard with 4 banks so you still have the ability to put in more memory later without removing your current ones, I'd go for the dual mode rather than conserving one additiona slot.
PC CASE - unknow(I havnt decide which one to get unless I buy full tower with core 2 duo in it on ebay.
One thing to keep in mind: there are many affordable cases, but pretty much all the cheap(ish) ones come with very poor powersupplies... A lot of the times you can save yourself a lot of headaches by either:
1) Buying a more expensive case with a decent namebrand powersupply
2) buying a cheap case, throw away the powersupply it came with and buy a decent one seperately
A mediocre powersupply can lead to an unstable/crashing computer due to varying power levels, or can have a significantly shorter lifespan, or have a cheap fan that can be much louder than a properly designed/engineered power supply... Mind you, you may get lucky if you get a cheap one, but overall there is a fairly big quality difference between the good ones and low end ones.
It's all too easy to blame windows when your computer crashes, but in too many instances it's really the hardware that's at fault.
One final thought: Keep in mind that computers are one of the most fraud-sensitive things you can find on ebay. There are *tons* of hit-and-run scammers that steal other peoples accounts (remember those nice phishing scams, emails claiming to be from ebay telling people to 'update their account information'?)
Even when you deal with someone with 100% positive feedback, there's still no guarantee that it's not a freshly stolen account with someone waiting to take your money with no intention of shipping. Laptops, HD TV's, LCD's and computers are the most popular items among those scammers since they are so expensive... Just be careful. :-?