Everyone should take 5 minutes and really read Dave's post above from start to finish. Those are very wise words from a very wise man. I second everything he said in the post including the negative remarks about combo machines except for the first 5 items on his list.
While I agree that for most machine shops the lathe should be first and that you can make any tools you need with a lathe, I personally, think a mill would be #1 on the list. As an apprentice machinist it would be very instructive to "build your own mill" from a lathe, however, I don't think that level of instruction is required for most FIRST teams. Our team has access to both a (very old wornout) mill and a lathe and while we use both because we have them I think we could get by better with just the mill than the lathe. We tend to make more "flat" things like brackets with slots or counterbores than we do "round" things other than shafts and spacers. Any of the shafts and spacers we have made so far this year could have been made with a hand hacksaw and squared off to length on the mill using a vise or v-blocks and an end mill. It would have been much more difficult to cut a keyway along the length of the shaft with only a lathe. The counter bores could be done on either the mill or the lathe but the mill took much less setup time. While it is possible to do some pretty nifty things on a lathe only if you also have a 4 jaw chuck and a compound mounted vertical x/y table it is just so much easier on a mill. To each there own, that's just my opinion. The bottom line is either way if you get a lathe then about a week later you will want a mill and vice-versa.
Another bit of advice when purchasing a lathe is pay attention to the spindle bore. The larger the bore the larger diameter material you can poke through and work with and the less you have to rely on a steady rest farther out from your chuck.