I built three 5.0’s this summer. Dressed up like a 289. The guys that purchased them were very happy with their 289 replacements.
Key component is factory roller cam.

I’m on a very tight budget so I’m looking at low milage used. Probably a pick n pull deal. What years/models should I be looking at.

My thoughts would be, what's currently done to the 289?  If its a solid running engine I think you'd be better off to make some upgrades to it vs. swapping it for a junkyard motor without rebuilding it.  I don't trust anything that comes out of a junkyard.  That vehicle ended up there for a reason, often because the last owner got tired of fixing it, couldn't figure out what was wrong with it, etc.  Sure, some were involved in wrecks and might be low mileage, etc., bot how long's it been sitting there?  The last 5.0 was installed in 2001, that's now 22 years ago (going on 23). 

Another thing to know is that the GT40 heads only came on '96-mid '97 Explorers and Mountaineers.  After that it was the GT40Ps.  The exhaust ports are raised on the P heads and standard headers probably won't fit (they don't in the Fox body cars).  There is also strict limitations on cam lift due to exhaust valve rotators.  They flow decent, but you need to do some stuff to them to make them work for anything but the mildest of performance use.  These were low RPM truck engines after all.  The more money you spend on them to closer you get to the cost of entry level aluminum heads. 

So the real question would be: how tight is the budget?  Another option is check out Craigslist, FBM, eBay, etc.  Sometimes you find decent deals.  I'd be wary of motors sold there though.  Heads, new parts, etc. are probably safe. 

No really...
.if the 289 is still good and you just want a little more  umppph....what about a stroker kit ?
The cylinder skirts are shorter on "SOME" 289 butt the stroker crank(and associated pistons  will work  (the 331 one)
I think its a 3.25 skroke.
The piston will just be at the very bottom of the cylinders.
Just this alone with whatever else you have on the 289 will prolly get you sideways in the first 2 gears !
May be cheaper than buying a crate engine or even going through a 5.0 out of the junk yard.
Food for thought............(You could make old Sal happy with a big-old snotty camshaft butt that's up to you !!!)
6sal6

The downsides to building a 289 is the potentially shorter cylinder skirts (not sure how you would know that prior to a teardown) AND lack of a factory roller cam.  Cost wise you can probably go through a whole 5.0 and refresh it for the cost of a stroker kit and install in a 289, AND the big issue is that the stock heads will be inadequate for the bottom end now.  Assuming GT40s or GT40Ps they work great on a 302.  Going bigger you would really need to port/rework them, at that point you're bucks ahead to buy a set of Edelbrocks.

I considered stroking my existing 289, but decided to go with a 5.0 based stroker instead for the reasons mentioned.  I always assumed I was buying heads, so all things basically being equal I saved considerable money with the factory roller setup

This is how projects get out of hand, especially from a cost standpoint.  Your cheapest option would be to just add a cam, headers, intake, and tune the carb and distributor in the existing 289.  Heck, you could add a set of heads to that list and still be under the cost of an engine swap.  After that its probably a fresh 5.0 with GT40 heads and a better cam.  Then a 5.0 with cam and heads.  On a tight budget I think I'd stick with stock displacement bored as needed to get clean, straight cylinders (302 might become a 306 due to an over bore, etc.).  Strokers need clearancing, balancing, and you may need a new balancer & flywheel. 

That clutch linkage boss was broken off the  5.0 block I used for my 331 build. My local engine builder had no use for it and gave it to me free, he did change for decking, line bore cylinder bore etc. though.
My AOD did not need it.
Scrounging around may get you lucky as well.