Edit: Nevermind my recommendations... You said on the cheap. Just get an old Windows PC.
Raspberry is gonna be slow. Stay away.
Sounds like you are gonna need a Windows PC to do all that without a fuss.
I'd go for one of these but they still need memory, OS and a storage drive.
For SSD: http://www.amazon.com/Intel-D54250WYK1-i5-4250U-Processor-Power/dp/B00H3YT8CC