If you want to join the military but you could also be looking at a good job, then I would do both. Accept the job and join a Reserve / Guard unit.

Go ahead and start with the trading desk and get going with it. After things have settled down with whatever changes you have had to make, then start talking to recruiters.

What you need to look for is the available opportunities in your area, and a recruiter can help you with this. For example, if you have an Army base close to your area then there is likely a lot of local Army Reserve opportunities available. If there are no local Army Reserve units, then you will need to look at National Guard units. Though I'm using Army as an example, you could do the same with any branch which has equivalents (and again, the branch will largely depend on local opportunities.)

Once you have located the local units which you could be based in (or close enough by commute) then try having the recruiter take you to each of them to talk to someone who can tell you about the needs of that particular unit. Hopefully that person could also tell you a little about the jobs available. You will probably find that the unit will have some needs which are more critical than others and this might mean the difference between being being bored with nothing to do and being active and needed.

The reason I suggest starting out as a part timer is because you have the best of all worlds. If you go into basic training / AIT and hate the military, then you get to go home and only have to deal with the military one weekend a month. If you love the military and feel that you want to go full time, then you have the option of making that switch.

Make sure you don't get pressured by your recruiters and MEPS. The recruiters will try to get you to go full time and MEPS is where you land your MOS (job.) I'm not sure exactly how MEPS work but when I went into the reserves I had to pick from a list of open jobs available in my area. If there are no open jobs that you like, I'm not sure what options you have. That is why I suggest you speak with a unit before you go, so that you can get a good idea of what is needed and what you will be doing.

I went into an aviation unit (Chinooks) and it was a lot of fun. The reserve unit I started out with was well funded and did a lot of work for the local community. For me, that meant free helicopter tours of places like Mt. Ranier. ;)

Another reason for checking with your unit is that you can see how active and how well taken care of they were. I served in two different units and the differences were like night and day. The first unit (Chinook Reserve unit at Ft. Lewis) was very active with most of their Chinooks in service and I had people fighting over my time for helping out in different areas. I could have easily landed a full time job there if I wanted to (another possibility, you can work full time military even though you are technically a weekend warrior.) The next unit I served with (Blackhawk Guard unit in Pheonix) had a lot of inactive aircraft and I hardly did anything.

From what I have seen I believe Reserve units are better funded but I could be wrong on that. The pro's for the Guard units is that they are more diversely located and I believe they have more benefits such as discounts on the state public schools.

Good luck and take things slow. Make sure you don't get rushed or pressured into anything.

EDIT: One issue you might run into is that you will have to take time for training. This might be a deal breaker for you and / or your job. You have some choice over your time away with the MOS you select. My aviation MOS was supposed to be something like 7 months on top of basic training but that was shortened quite a bit because we had a small class of people who were all college students (we were much stronger in the classroom environment than the typical Army recruit.) If you couldn't be away that long then you could pick a much shorter MOS.