I'm pretty well known fro not telling people what they want to hear, so let me offer a "reality check". I certainly don't wish to discourage a "young gun" from getting into this hobby, but rather wish to impart some wisdom learned from making some of the same mistakes in my youth.
First off, EDUCATE YOURSELF. Get and thoroughly read "How to Rebuild your Small Block Mopar" by Don Taylor/Larry Hofer then get "How to Hot Rod your Small Block Mopar" by Larry Sheppard. This and other forums on the internet certainly also contain plenty of "free advice". A factory service manual reprint is also a must.
A 273 will be more expensive to rebuild than a 318 or 360. Why? Because they were the least produced LA engine, and have been out of production the longest. Parts such as pistons are low sales volume pieces, made in small batches by very few suppliers. Basically a custom part. Egge's prices are quite reasonable for what you get, and their customer service is good. I've ordered from them myself.
If your budget is only $800-$900, strike the word "rebuild" from your vocabulary. You can't get there from here. You MIGHT be able to overhaul or "freshen up" an already running engine for this, but even then I have my doubts. By overhaul I mean a complete disassemble, clean, inspect and reassemble replacing only those parts which are damaged or worn beyond spec. Figure a complete gasket set, rings, bearing inserts, timing chain and a valve job. Machine shop labor should be a quick bore hone and crank polish. The above assumes the bores and crank journals are reasonably round and taper free. Head work will be at a minimum new valve guides, valve and seat resurface, and spring shimming. Add $$$ for new valves if the current ones have worn stems, are burnt, bent, or have already been ground. Heads can suck up $500 real quick.
$800 should buy you a running 318, and a couple cans of red paint. If you have an auto, you may have a converter hub miss-match, but this is fairly easily dealt with.
There is no such thing as "numbers matching" before 1968. So don't lose any sleep over that. Anybody who is smart enough to tell a 318 from a 273 by looking at it won't bother asking you what you have, or if it's original.
If you don't want to "over spend", stop right now. We're talking about a 47 year old economy car which was never "rare". If you want to fix up and drive an old Barracuda, that's a noble goal, and you can have a lot of fun doing it. But I cringe when I hear people talk of older cars as an "investment". I have exactly one 1965 Dart in my portfolio, and it is most certainly in the liabilities column. See my signature below.
If the 273 runs now, spend your money rebuilding the front end and getting rid of those 9" front drums. If the car has typical Minnesota corrosion, consider spending the cash on a rust-free body sooner rather than later.