1) Bolt action, full sized battle rifle
2) Fires a full-power, 30-ish caliber cartridge
3) Reasonably accurate (minute of pie-plate)
4) Moderately cheap (under $200)
5) Available ammo
Getting 4.) and 5.) together kills a lot of the options.
The one rifle that really satisfies all of the conditions is the Mosin Nagant.
1) Bolt action, full sized battle rifle The 91/30 is the longest of the rifles, but consider that the M38 and M44 carbines have 20" barrels, more of a rifle than a carbine. At any rate:
2) Fires a full-power, 30-ish caliber cartridge The 7.62x54R fits the bill nicely.
3) Reasonably accurate (minute of pie-plate) If you mean at 100 yards, event he roughest of Mosins that I've seen will hold this. If you want better, don't order online, go to a store where you can inspect the rifle. Look closely at the bore if you want a shooter. Some of the best bores I have are on Mosins with really rough wood, so outside appearance is NOT soemthing you can judge it by. Also, look for a counterbored rifle.
Now, a lot of guys will laugh, but the Russians counterbored the barrel when the crown got messed up. It was cheaper and easier than recrowning, and leaves a nice crown inset into the barrel, with the end of the barrel acting as a protector. Counterbored barrels will tend to outshoot the "better" fully-rifled barrels. This was a normal rearsenaling feature and is not a Bubba job.
4) Moderately cheap (under $200) You could buy 2 or 3 NICE Mosins for $200. With the 91/30s you also usually get an accessory kit which has the bayonet (these guns were sighted in with the bayonet attached and may need to be resighted if you don't want to mount the bayonet), an ammo pouch, oiler bottle, multi-tool, cleaning rod handle for the (should be) mounted cleaning rod.
5) Available ammo Surplus ammo is dirt cheap. Commercial ammo is dirt cheap. Brand new Wolf is $8/20 here and the better, Barnaul ammo is $7/20.
That's the best deal around.
Now, if you're willing to go over on
4) Moderately cheap (under $200), a GOOD Mauser will fill all of the above, and the ammo is dirt cheap.
If you're willing to go over on
4) Moderately cheap (under $200) AND
5) Available ammo, then the No4 Mk1*, Mk1/2, Mk1/3 or Mk2 Lee Enfield is the way to go.
The Enfields out there for real cheap that I've seen are REALLY rough, I'd stay away from them. But if you're willing to throw maybe another $100 into the rifle, you can get some really fine No4 rifles. The best I have are from
BDL Ltd . The surplus ammo has pretty much dried up for now, and I'd recommend handloading over buying the fairly expensive commercial ammo.
Case for the additional expense of an Enfield:
1.) The slickest, quickest action of any battle rifle, better than most commercial rifles.
2.) 60 degree bolt throw rather than 90 degree.
3.) 10 round magazine capacity
4.) Stripper clips readily available.
5.) Finest battle sights of any bolt action rifle.
6.) No-drill, no-tap scope mounts are cheap.
7.) All of mine have been excellent shooters. Think pie plate at 300 yards.
But honestly, if you want an inexpensive shooter that has modest accuracy, the Mosin is your ticket. Just beware, they tend to multiply in the safe when you're not looking.