We are in exactly the same position as you(maybe a bit more space). The sponsors you have also are important in this decision. This year we obtained a rather large lathe(close to full size) and a small mill. We haven’t used our mill that much(it’s less useful and less powerful so we send many parts off to a machine shop).
I would high recommend against the 3D priter. IMO it is a waste of money that can be used on machines that may be less versatile but can machine larger parts. There really is no reason that you NEED a 3D printer. If space is limited, you also want to make full use of the space you do have. Our most important tools are our drill press, chop saw, arbor press(3 ton will seem large, but it is basically the smallest you can go without going too small), vices, lathe, and disk sander. Once you have those you can start adding on machines. Bandsaws are nice(especially horizontals for cutting down stock) and you can add a mill later.
If you have a machine shop sponsor or waterjet sponsor your needs will vary. We usually send our tubing and complicated CNC parts to our machine shop. However, this is generally unnecessary. If we wanted to, we could do 95% of our tube in house on our drill press and chop saw, albeit with a bit less accuracy. The hardest part would be doing our bolt pattern(which you could make a dig for if you really needed to). If we needed to we could probably use less or no CNC parts in our design. If you can get a waterjet or laser sponsor(really quite easy to find one willing to sponsor you) it would help a lot. 2D machining is a lot faster than milled or lathed parts. We use a ton of wterjet parts in our design because of how versatile the parts are. One way of building is using custom waterjetted gussets and match drilling your tube. For a low resource team this is very accomplishable and from what I hear quite similar to how 2056 initially build there robots. The most important thing to remember is that you should design around your machining resources, not the other way around.
Tools and how we use them:
Lathe: essential tool. it is the best way of making round parts. with it you can machine shafts, spacers, standoffs, rollers, and hubs that are not possible to do well on any other machine
Chop saw: essential machine to cut down stock
Drill Press: We use to modify waterjetted parts. Can also be used for tube. ESSENTIAL TOOL
Arbor Press: Essential tool to press thing sin and out. We use it to get press fits on our bearings, hubs, rollers, etc. We also use it to broach parts in house Really,really, really useful machine that can get you out of a lot of tricky situations
Vices: Hold stuff. Pretty self explanatory
Disk sander: round edges. can be used to grind lathe tools(cheaper than insert bits, we like inserts)
Mill: used to ream waterjetted plates, and machines some of our misc easy to machine tube. Used for accurate cutoff and holes(i.e bolt pattern). We rarely mill stuff(though occasionally when we are in a bind we do. hoping to use this machine more next year). IT isn’t needed but we’re glad we have it.
We don’t have the rest of these tools, but if we had them this is what we would use them for
Vertical Bandsaw: cutting stock, cutting more complex shapes, it is a bit more versatile than a chopsaw but also permanently takes up space.
Horizontal Bandsaw:Used to cut stock. There are some nice models that you clamp the stock in and leave the machine. The machine automatically turns off when it is done cutting
The last thing to remember is that for large machines like mills and lathes you want to budget as much money for the tools as the machine itself. This includes workholding, cutting tools, etc.