Soooo many rifles, so little time! I see you live in Springfield, OR. Have you ever visited the ARPC twice-a-year gun show held at the Linn Co. Fairgrounds? Huge show--you might find something there. I think the next one is in March or April. Much larger and better show than the one periodically held at the vet's hall on MLK Blvd. in Eugene.
I'd hesitate to make a hard and fast recommendation. I've enjoyed many of them. I guess my current favorite is the Czech VZ-24. Like so many have already said, the Swiss K-31 is a good one. Did anyone mention the Lee Enfield No.4? The Turk Mausers are good, but long, about 6 inches longer than the others mentioned. Krags, 1903 Springfields, 1914 and 1917 Enfields, all great fun. Most Mausers, no matter where made, tend to shoot well if in good condition. It's going to depend on a combination things--what you happen to run across that has appeal for you, cost, condition, etc. Check the bore for condition, muzzle crown for nicks, stock for cracks, headspace if possible. I'll bet that after you get your first military rifle more will follow.
Hard to say what you can get for $300. That's probably a good middle-of-the-road figure. Some of these might run a little more, up to about $450 for a nice one, but you should be able to get a Turk Mauser or an Arisaka for less. I hope you'll revisit the thread and tell us what you settled on, what it cost, and how it works out for you. There's always the unexpected bargain.
DG