Some things you need to look at before blowing a bunch of money on tools is what do you have to work with, and where do you feel you're currently falling short?
First is space. How much space do you have to work with that you can permanently setup with your tools/machines/workbenches? If you have very little, you'll want to stick with small hand tools and a locking tool box with some cordless drills, and a nice bench vice(actually just get a nice bench vice, they're always good).
Secondly what mentor support do you have? I see you're looking at welding equipment, mill, lathe etc. These tools are great, can expand your capacity, and can be very safe when used properly. When used incorrectly things can go very bad very quick. If you don't have at least one mentor(better 2+) who plan to stick around and help teach and supervise the use of these machines then getting them will be a Very Bad Idea(tm).
Third Power, small bench-top machines can run off standard 15A 120V outlets. Larger lathes and mills will often require 240V, triple phase power, and sometimes even higher voltages. Part of why these machines sell for around the cost of the bench-top hobby equipment is because a hobbyist cant as easily support their power requirements. Welders can be particularly challenging as well. Even ones that run on 120V can draw a lot of current and pop breakers if there's other stuff on that circuit(do you really know the circuit layout at your school?). I can promise you having to call maintenance to reset breakers for you is not going to win you friends.
Finally when looking at a Mill and Lathe in particular do not forget the cost of tooling. To get well tooled and be able to start working with these machines will cost you AT LEAST what you spent on the machine in accessory tooling.
If I were starting with nothing, and had mentors with only some general knowledge of tools here's the order I would spend my money:
Tool box: something like this:
http://www.grizzly.com/outlet/6-Draw...l-Chest/T10140
Mechanics Tool Set: craftsmen is a good middle of the road brand, you want full metric and SAE wrenches ratchets and sockets as well as a good assortment of screw drivers. Buy extras in the sizes you use most.
Hex key sets: Again I reccomend craftsmen for mid range, go for snapon/mac if you can afford it. Again you want both SAE and metric with extras in your most used sizes.
Cordless Drill: There's a lot out there that's great, I think DeWalt makes some nice lithium battery drills that most folks I know with them love. If you buy multiple buy the same so you can buy spare batteries most efficiently.
Full Drill Set in metric or SAE, both if you can afford it. These are usually ~100 dollars and have on of everything up to about a half inch dia.
Center Punch
Measuring tools: Big to small: some good length measuring tapes, a couple yard sticks, some metal ~ 1ft rulers, I also find some small 6 inch rulers useful, 6 inch digital or dial calipers(if you're a glutton for punishment verniers).
Combo square:
http://www.grizzly.com/products/Econ...n-Square/G8072
Hack Saws and a variety of blade types
Assortment of Files: lots and lots all different shapes and sizes you can never have too many.
Dremel or similar tool. There's really no limit on what you can make a dremel tool do.
Pliers: standard, vice grips, needle nose
Hammers: Ball peen in large and small sizes, rubber head mallet, plastic face, or even better a deadblow hammer.
Good wire strippers: not just the cheapest you can get, the ones that pull the wire apart automatically can be quite nice.
Good crimp tool: Again you want something that's not going to leave you stranded on the field. Every years teams are bit by mysterious electrical problems traced back to bad crimps.
Digital Multi-Meter: Now that you've wired it up, it helps to be able to test it. Cheapo units will do, but go for a higher end unit if you can afford it.
Pop Rivet Gun: nice and light fastener setup, be sure to research when and how to use these to maximize their potential, I believe there's a lot of literature on the topic here on CD.
Soldering Station: I'm partial to Weller, but you'll want something you can control the temperature and get a good solid solder joint
Workbench: Something sturdy
Workbench mounted vice: Biggest and strongest you can find. Ideally this thing should be able to laugh at a jackhammer.
Sawzall: can be a poor man's replacement to a bandsaw for chopping through stock if you don't have the space. Really useful when you need to cut stuff off the bot without disassembling.
Jigsaw: Really great multipurpose tool for cutting lines or shapes in sheets of material.
Drill Press: Radials are nice, you'll want something that can go pretty slow when needed: floor or bench model:
http://www.grizzly.com/products/5-Sp...ll-Press/G7946 http://www.grizzly.com/products/5-Sp...ll-Press/G7945
Drill Press Vice: There's a bunch of different designs pick what you like.
Drill Press XY Table:
http://www.grizzly.com/products/6-x-...de-Table/G8750 I bought this one for my team last year, and it can make precision drilling a dream compared to a hand drill.
Tap and Die Set: You can go for both SAE and metric, or just pick which you want to use, and buy the other piecemeal as needed.
Bandsaw:
http://www.grizzly.com/products/4-x-...-Bandsaw/G0622 Cutting through huge slabs of metal with a hacksaw is no fun, make life a bit easier on yourself.
Don't forget to buy blades and bits for many of the things listed here. Getting well outfitted with a good base of tools can be more important than playing with the more exotic tools like CNC, Lathes, Mills, welders 3D printers ETC.
If you have all of the stuff above, and still have the proper facility, and mentor support begin looking into more exotic tooling.