Join Date: Jul 2015
Location: Pennsylvania, USA
If you're comfortable buying S4S (pre surfaced all 4 sides) lumber from a mill or home store and working with plywood, you're mainly going to be concerned with cutting, profiling and joinery. You've probably figured out by now that the table saw will be used a lot in most of your projects.
I'd personally skip the jointer and planer in your situation, at least until your budget expands. Don't worry, that happens surprisingly fast if you're anything like the rest of us here.
For making the profiles, you'll definitely need a router and table or shaper. I used a very small $100 router table from Lowes for many years, but I can tell you that when I upgraded, I feel safer and my work is more accurate. If you can bump a router table build (many plans available here and throughout the internet) or find a nice quality used one, I'd recommend it over a cheap plastic one. For the router, I'd recommend at least 2hp plunge with a 1/2" collet and adjustable speed. 2hp is small, but probably do-able for raised panel bits.
For joinery, there are lots of options. In your price range and for your projects, a few options that come to mind are biscuits, dowels, pocket screws or spline joints. Clamps will eat up more than you think out of your budget. You need good screw-type clamps (pipe clamps, bar clamps) for glue joints and maybe some squeeze clamps for assembly.
This is what I would buy for your budget/projects:
Router bits $150
Router table materials (build your own) $250
Kreg Jig (for pocket screws) $140
RO Sander $60
That covers the basic tools, but then you'll need to budget for consumables (like sand paper and hardware) on a per-project basis and materials. You also did not mention finishing, but you'll need applicators (brushes,etc) and finish.
This is my opinion and other will have valid opinions as well. There's lots of ways to accomplish a task in woodworking. A lot of it is personal preference.