I served 6 years in the Marine Corps, with my final two working as a liaison between the monitors (the folks in Quantico who decide what specific MOS each new recruit receives) and the recruiters. So unless standards have relaxed significantly since I got out about a decade ago (and judging by friends who are active duty recruiters and the economy, things haven't relaxed), no matter what a recruiter tells you, you will not be able to go Recon with a misdemeanor conviction on your record, let alone a felony. You will need a minimum of a TS clearance to go into Recon and you will not be able to obtain that with nearly any conviction on your record - especially any conviction as recent as this one that you are up against.
Regarding going into the Marine Corps Reconnaissance program, they actively recruit Marines from any MOS, not just the 03XX field. In fact, just based off of my experience with those I knew who went into Recon, the majority did not come from the infantry. While many were in the infantry, I'd wager than an equal number came from communications (06XX), intelligence (02XX), signals intel (26XX), linguistics (27XX), tankers/AAV (18XX), data/comm (28XX), etc. Recon units operate in much smaller groups than your typical platoon therefore often need Marines who know how to do more than put lead down range.
Would you be able to make it into the disbursing field with this on your record? Probably, but that is a very small field with only a few billets available each year (relative to many of the other fields in the Corps) and when the monitors are looking at who to place into the disbursing field and they see somebody with a conviction on their record and somebody without, all other things equal, you can pretty much guess who they would choose.
Even with the conviction on your record, there are still plenty of good opportunities available and I personally would advise strongly against going in as infantry. I personally cannot think of one advantage to being in the infantry, but if that's what you really want, I would advise going in as something else, giving it a couple of years, and then attempting to make a lateral move into the infantry. Because the turnover is so high in the infantry, they are always looking for NCOs with a bit more experience to come into the field. If travel and seeing some "action" are your big concerns, one of the advantages to the Marine Corps over the Army is that it is so much smaller and nearly every unit is a deployable unit. I spent my time as a paper pusher but did so all over the place including cleaning up after an earthquake in Turkey, earning a CAR in Kosovo, auditing Marines at U.S. Embassies throughout Asia and the Pacific, etc. In the end, doing the "cool" stuff comes down to what unit you get attached to more than anything else.
I know it may be too late since your court date is sometime today, but if you are serious about joining the military, I would do everything in my power to get the charges against you dropped completely. I'm no lawyer and don't know what state you are in or how serious a Theft III charge is but as others have mentioned, it would probably be a wise idea to have a lawyer with you. Let the judge know you are considering joining the military, are willing to do extra community service, etc. Basically, the fewer blemishes on your record, the better chances you will have at getting one of the more coveted jobs.
As for JustinW's comment about signals probably not being such a cool job anymore, I can say that at least in the Marines our enlisted signals intel folks are definitely out on the front lines (I'm sure there are of course some in the rear too). Of course there are probably a lot few signals and crypto folks these days than there were 20 or 30 years ago so it's a tougher field to get into initially. Whether we were aboard a ship or on the ground somewhere, I remember our signals folks were always getting sent out on operations - often attached to a small Recon group or some other small detachment.
The OP had mentioned in one of his posts about tuition repayment options through the Marines v the Army. He is correct that the Marines do not have a tuition repayment plan. They used to have a $75k Marine Corps Scholarship available to certain recruits which might be something to look into. Also, if you are currently a junior at your university, you likely do not need quite so many classes to finish your degree and while you are in the Marines, they do have 100% tuition reimbursement (unless you fail the class and they take the money back from you) that could be used to take the final accounting courses you need to get your degree while you are on active duty.