Tig welder,OA torch,couple of drill presses,surface grinder,and throw in some modest wood working equipment if at all possible. After that...... some modest sheet metal equipment comes in durn handy here. A squaring (stomp) shear,finger or press brake,and rolling machines. Oh yeah,nice big H frame press gets used here often enough to warrant the real estate.
You sort of need a "working list" of items you're looking for. Read as much as possible about them,learn what makes'm tick. Because when deals roll around you usually don't have time to do the research..... there's times to be patient,and times to bust out the $100's when it comes to buying equipment.
Team up with guys looking at equipment.... just like if you're buying used cars,don't go alone. Mores eyes are better but you gotta go looking. Not disparaging machine dealers,they can be a fantastic resource but.... there are reasons their machines aren't moving. It's a lot like fishing and hunting,the more you do it,the better your "luck". This is why you so often hear about guys buying their first lathe(mill,?) and then all of a sudden there's several more popping up. And they looked for 3 years to find the first one. You have to cultivate your machine spidey sense through research AND getting off the couch to actually look at pcs. The contacts you make are like friends.... they may not have the piece you're after but give you a line on a low mileage XYZ machine. Good luck,my wife cringes at the mention of a road trip,haha.
Edit; wasn't 10 minutes after posting above that I was surfing some of my favorite machinery venues and found/bought a sorta unicorn piece. Mid 1940's,needs some serious TLC. I don't want it but one of my sons is doing backflips this a.m. Don't need all the details but it was first posted late Friday night. If it was 6 months ago(pre covid) it would've been snatched up. Point being,I knew what it was and what it needs and ready to buy..... not dicker over price.