IMO $350 is not really a budget for a decent CNC... DIY or otherwise.
Depending on the size a decent framework, drive system, and linear travel CNC is going to probably be more than your budget. The 80/20 frames I build have a working envelope that is anywhere from 18"x24" all the way up to 4'x8'. Even the smallest size machine will easily wipe-out that budget.
Electronics are also probably going to exceed a $350 depending on what you go with as far as drivers and motors.
Lastly, software can be open sourced so, you can probably make that happen. If you were to work with what I've suggested earlier, I think Vectric charges around $600 for VCarve and Mach 3 I think still costs a hundred or two.
HTH
I depends on what you want to do. My Chinese CNC router/laser is just about $200. The work envelop is tiny, but within its limits it works great. You can scale that up to a decent size for $400. You are definitely not going to go 4x8 at that price.
On a $350 budget, I would stick with 2x2 or smaller. GRBL based controller with TMC2208 stepper drivers, Nema 23 motors, 36 volt ANTEK power supply, and 8 mm rails. Use Fusion for your CAD/CAM and BCNC for your control. 80/20 is good, but over kill you can make the machine out of plywood.
It would not be the fastest or stiffest thing, but it would definitely get the job done. I ran my mill of this setup for a while
Linky. I out grew it quickly on the mill, but it worked and I had less the $200 in it (Not counting the mill)