I'll start by saying the obvious comments from the forum first
1) If you can fit a Bridgeport knee mill, do so.
2) If you can purchase a well-cared-for used Bridgeport, do so.
3) Are you sure you can't fit or buy a Bridgeport knee mill?
4) Read the many threads already in place. Cory is one of the resident experts on this subject.
Now, on to my comments...
First, I'm not a fan of machine tools in the pit. I don't like the idea of undersizing machine tools to be mobile when it sacrifices the working envelope. I also don't like having a huge liability (thousands of dollars of equipment) that could be stolen.
5) I am a huge fan of the Bridgeport knee mill. I'd love to have one, but I move around quite a bit, so I bought a PM-30MV-L for personal use.
6) If you can't fit or buy the Bridgeport, I'd recommend getting a bigger mill than the LMS HTMM. It is suitable for very small projects. For $1800, you can get a
PM-30MV-L from Quality Machine Tools. For $2400, you can get a
PM-45. Both of these mills are larger and will be more versatile. For the same price as the HTMM, you can get a G0704.
7) You aren't building a space shuttle. The
quality Chinese-made mills work well and are great for FRC applications. Be sure to disassemble, clean, and lube any new Chinese mill and you'll have a smooth machine. Unfortunately, this is where you learn where the cost savings come in (Bondo, hastily-done castings, etc.).
8) You might be better off with the LMS 8.5x20 lathe, but the lathe you identified is well-regarded. The 7x12 is the same manufacturer (SIEG) as the Harbor Freight version of the same dimension, but I believe LMS has higher quality standards.
9) Did you ask LMS if they will sponsor your team? Maybe they will cut you a deal
10) In any case, get the biggest that you can fit in the space and be sure to budget about $4-5k for quality tooling. You can get cheap endmills - I've had good luck with the $65-80 16 count set from Grizzly on our FRC team's G1007 (not recommended - round column), but they don't get as much use as the quality endmills in the Haas or Bridgeports.
Good luck!