If your existing engine is just tired and not broken, you could (or have a reliable person or shop) just freshen it up with new bearing, rings, timing chain, etc. Depending on mileage and wear, the cylinder walls might be tapered or out of round; it would need to be bored and new pistons installed. You would aslo need to have the heads rebuilt ie. valves ground, maybe valve guides repaired, etc. Then it could cost as much or more than a basic crate engine.
You can get a new universal 350 engine (part # 10067353) through most GM dealers for around $1300+. It might be as cheap as a total rebuild of your existing engine and would come with cylinder heads but without accessories such as power steering pump, etc. which can be changed over from your existing engine.
If you and/or friend(s) can do the engine switch, additional cost would be minimal. If you have to pay a shop to do the switch, you would have that expense also.
For a little over $2000, you can get a new high output 350 engine rated at 330 horsepower through GM (part number 12486041).
If you have deep pockets, you could get a 383 crate engine from GM or other engine builders or other high horsepower engines. In this case, get a copy of the October issue of Chevy High Performance magazine and look at the special section as well as all the regular ads throughout.
One thing to keep in mind - most crate engines offer a warranty for non-racing use. I'm sure other Forum members can give you additional ideas and information as several regulars have done engine rebuilds and replacements. Most importantly, make sure you know what you want from the new engine, do your homework, and don't rush in to anything.
Good luck on your project and please keep us posted.
Terry