I think you need to quantify your need. For instance, "many more drills" could mean two or twenty. Look at how many sub-teams will be working on the robot and how many will be required to use the tool.
What productive capacity can the tools be used for?
I honestly don't believe in welding for FRC robot frames anymore and I find it a risk for students that is unnecessary (PPE, ventilation, sunburn). If this is a construction method, I feel it's best to outsource to a properly trained professional. I'll caveat that with the understanding being there are vo-tech students which may be able to accomplish this task as the exception.
Judging by what you've laid out, I would suggest taking your list and narrowing it down based on the importance of the tool, the number of tasks it can be use used for, and the quantity/cost associated. For example, a regular cordless drill can be used for 5 tasks in the build vs. a specialty tool that performs the same basic function, but isn't required (e.g. right angle drill). This would rate the cordless drill higher than a right angle drill.
If you do get cordless tools, look at the brand and the tools available. Stick with one brand to save on battery charger footprint, as well as allow for battery interchangeability.
My personal recommendation for a small-medium team (20-30):
Tools requiring only hands:
1. Auto-centering punch (qty 2) $3 each at Harbor Freight
2. 14.4V Drill - you don't need 18V and the lower weight will be nice over time (qty 3) + drill bits in common sizes (clearance and taps for standard hardware)
3. Ball-peen hammer (qty 2)
4. Straight Edge/T-square (qty 2)
5. Digital 6" Calipers (qty 3) ~$15 each Amazon/HF (Also buy a 100pk of batteries for ~$8 from Amazon, the LR44 die very quickly in the HF units)
6. Vise Grips (qty 4-6)
7. Hack Saw (qty 2)
8. Allen Set (usually cheaper in the set) (qty 3)
9. Socket Set (personal preference; cheaper in set)
10. Additional sockets and wrenches in common sizes for your robot (for#6, #8, #10, 1/4" hardware)
Shop tools requiring facility resources:
1. Drill press
2. Band saw
3. Press break
4. Sheet metal shear
5. Arbor press (bushings and keyways) NOTE: keyway broach sets are expensive.
6. Belt sander
7. Disc grinder
8. HF 7x12 lathe (#93799)
I highly recommend the Harbor Freight tool carts (with the associated high reviews). They are high quality and very durable.
I'm absolutely certain I didn't get everything, but hopefully you find my post a little useful.