Plexi-Glass rofl. Seriously bro use a real case. I don't think you understand how complex computer cases are. Building with plexi will be a nightmare and will end up being more expensive.
You're in the used parts market with a $300 budget my friend. Craigslist, buy sell trade posts like the one on this forum, etc. For 300 bucks you should be able to pick up some 4 to 10 year old parts and put something workable for minecraft together. Don't forget that you will also need an operating system and that alone is $100 for Windows 10. You might want to go with Linux or Steam OS to keep your costs down as these are both free operating systems. Or maybe you can get somebody to sell you a previously enjoyed retail license for windows 7 8 or 10.
Around here I could put together something like this for $300
Phenom II X4 or X6
8GB of RAM
250GB hard drive
GTX 750Ti
A case
As far as a DVD/CD drive, nobody uses those any more. They're obsolete. I haven't used mine since about 2011. If you really want one they are like $12-25 NEW and $5 used. That's for a burner too. Just super cheap these days. It literally costs more to buy 25 blank DVDs than it does to buy the drive that burns them.
A tip I can give you based on my own experience is this- the day after christmas is the day for guys like you. Families buy new computers for christmas and give them to their families on christmas day. The day after christmas if you walk through residential neighborhoods you can sometimes find five, even ten discarded computers on a long walk (getting your parents to drive is better. Cars have trunks. Computers can be heavy.). These discarded computers almost always work in my experience, and even if they don't they usually have some still-good parts in them. I have seen some computers discarded like this with CPUs like Q6600s (A CPU which would suit your needs) and graphics cards as good as 8XXX and 9XXX Geforce cards (2007/8). Granted, often these parts are dead, but you see what I'm getting at. You go for a 1 hour drive, pick up 20 discarded computers, odds are you can put together a nice little system for yourself cherry picking parts. Hell, you might even be able to rip a windows license off the sticker on the side of one of those PCs and be up and running for an investment of whatever the gas your parents burned was and that's it.
Having said all that, if I was in your shoes, I'd beg my parents to spot me another $200 (plus taxes and shipping) and I'd grab this
http://www.dell.com/en-us/shop/productdetails/alienware-alpha/dkcwa05hbts
