HP model XXX has an i3 based system with 300w PSU for $550. You could get that and add a $120 HD7770 and have an OK gaming system.
OP: suggest you answer the questions for a suggest build. Like what do you use a computer for: video production? gaming? running a compute grid? fileserving?
For light gaming any Mid size tower (not small form factor, slim, etc) with a pwoer supply rated at 300 watts or more will get you started. If you can find a unit with a beefier power supply that gives you more simple upgrade options.
Prebuilt might have warranty seal , which means you' can't open it.
Might, but the IBM, Lenovo, Sony, Gateway and HP computers I've upgraded didn't have seals, instead they had manuals that explained how owners can open the case and add in more memory, PCI cards, disk drives, etc.
If you require an in-warranty repair (e.g. memory fails) you typically need to get back to their hardware config if you are sending in the computer. If however they are just mailing you the part then you don't need to do anything.
(I did have one incident years ago where the factory restore was incompatible with an upgraded video card, and I needed to swap out an ATI for an nvidia (or visa versa, I don't remember) to get the factory restore to complete. Thats the only problem I can remember upgrading pre-builts. I uses buy refurb rather than new. A prebuilt refurb is typically a good bit less than the equivalent quality parts purchased separately.)