Trying to get all 4 firearms for about $700 will be tough.
The closest would be these, in this order of purchase:
1. Find a used, not abused, Mossburg 12 gauge pump, in 3 inch magnum, with synthetic stock, for around $150.
2. Find a used, not abused, Marlin bolt action in .22 LR for around $100.
3 . The handgun will be pricey. I would look for a good used, 5-shot Rossi, with a 3 inch barrel, in either .38 P+ or .357 Mag. ($275?). Make sure it is tight and timed. Don't fall into the thought of using a handgun for dual purpose hunting, in larger calibers, with longer barrels. This is your CCW, and it is for lawful self defense only.
4. Get a used Handi Rifle, in .308 Winchester ($125 to $175?). Or, you may be able to find a used Marlin 336, with a beaten up birch stock, in .30-30, for about $200. If you want to break your budget, get a new Stevens 200 in .308. Quality for the price, but with a synthetic stock. ($250?).
All of these are popular firearms that are easy to locate on tables at any large gunshow. I have been at several shows where the first 3 of these items were on the same table.
Regards, Mannyrock