MOS selection occurs at The Basic School, or TBS, the six month initial training for all Marine Corps 2nd Lts. Therefore, yes, you can go Marine Corps Finance or Intel from USNA. However, you cannot go Navy intel, as this is considered restricted line.
It's possible to go Intel, but because it is Restricted Line, it's an option usually given only to Midshipmen who are not eligible for Unrestricted Line communities.
As mentioned MOSs are given around the 4 month mark at TBS. Yes, Financial Mangement is an option. When I went through TBS most companies had 3-5 billets for Financial Management. I had several friends who went this route and have done very well in the USMC and in the private sector for those who left active duty. There are several different types of Intel to select out of TBS; aviation, ground, human (not sure if there are more now or not as they re-designate/combine/reduce/add MOSs every once in awhile, plus there are secondary MOSs when you get down the road in career progression). The number of billets range per a company, but I think the average when I went through was around 20-25 total Intel billets per company. These numbers vary in each company based upon the "needs of the Marine Corps."
Navy Intel covers the full range of intelligence work. From air intelligence, imagery analysis, threat analysis for surface, sub surface, air, and a whole range of other items. If you google Navy Intel there is a load of data out there. The goal of the Academy is to commission Unrestricted Line Officers (SWO, subs, pilots, etc). Those who are found Not Physically Qualified (NPQ) during pre-commissioning physicals can select from the Restricted Line billets such as supply, intel, info ops (former crypto), etc. There are a variety of reasons Mids can be NPQd, but most are from injuries or illnesses they had while Mids, color blindness, height (some of the basketball players are really tall), or some other reason. Not sure on stats, but when I graduated I think we had about 30 Mids go restricted line mostly for color blindness or severe injuries/illnesses they sustained while Mids. But just because someone is NPQ'd does not mean the same thing in the USMC. Alot of Mids who were color blind went Marine Corps because there are more options for them. I had alot of friends who were once SWO qualified transferred to HR, supply and Intel. From my understanding this is not as easy to do now in the Navy, but it does not mean it is impossible!
