Oak is a specie of wood you shouldn't paint. The grain profile is too harsh. I agree w/ the previous poster that suggested using ebony stain - this is your best bet. Seriously, don't paint oak. (The common paint-able hardwoods are maple and birch.)
I got a miter saw before a jig saw or a circular saw. However, if you will be ripping sheets of ply at home, you should start with a circular saw. I got a corded one, which I now regret. Here are the power tools I would get in order for beginner woodworking:
1. Drill (you have one)
2. Miter saw (10" non-sliding, single bevel is just fine)
3. Circular saw
4. Orbital 5" sander
5. Jigsaw
6. Compressor and brad nailer (you could go w/ battery brad nailer if space is at a premium)
7. Table saw
8. Band saw
9. Planer
10. Jointer
11. Disc/belt sander combo or 3" handheld belt sander
12. 12" dual bevel compound sliding miter saw + stand
** A router is a nice tool to have, and you can buy it at anytime - I got mine before I bought a circular saw
Outdoor seasonal decorations will require simple joinery and should be assembled w/ screws. If you use glue, only use Titebond III - this is the only waterproof woodglue. It also happens to have the strongest wood bond among ALL glues. The tools you need are dependent on what type of decoration you make. A miter saw and drill will take you very far. A circular saw is great if you are working w/ pallets.
For drywall, get a few metal knives (they look like wide spatulas) and a metal mud tray. Use a file or sand the sharp corners of the knives down. For cutting, just use a utility knife. For driving screws, get a drywall bit for your regular drill (it should be less than $1 at Home Depot).
For garage shelves, have the store you buy plywood form rip the boards for you. Trim them to length at home on your miter saw.
Final advice: if you are mainly cutting 2x4's, skip the jigsaw - it won't cut through them safely, and the blades will dull quickly. Start with a miter saw if you are mainly using 2x4's.