What would you recommend to someone with a finance/economics degree and trying to become an officer (which branch of service and what job)?

I started out with a finance degree in 1988 and found my two computer language courses led to Army Signal and 30 years in software development.
You will bring a business view to the technical analysis that will help customers make decisions on what technology to invest in and areas to automate.
If I was starting again, I would lean heavy to cyber security. There are more jobs than people and the Army can't wait to train you.

People will blurt out Finance. Army Finance has NOTHING to do with Finance. Business finance is the acquisition of capital to fund projects And future operations (the G35 of money). The Army obtains its funds from a Byzantine process called the POM "Program Objective Memorandum", which is allegedly an articulation of requirements which looks eerily like your last year's budget plus or minus 10%. When times get tough, they cut it in half. That all goes up to OMB and becomes a DoD level budget. The executive branch puts together the budget, which the Congress votes on and turns into a law as either an Omnibus (many things) or if we are lucky, a National Defense Authorization Act for that FY. Law says it has to be complete and in the can in the May before the FY starts 1OCT each year. Last 20 years, that has been rare with very late budgets and continuing resolutions where the DoD is supposed to trundle along without exceeeding the last previously appropriated level. We don't acquire capital at a cost (corporate finance), except in some very rare MWR situations, which you will usually generally always never see.

What my FI officers did was cost accounting (the G33 of money, current ops). They did cash disbursements (to people or commercial vendors doing business with the Army). Moved money around between compatible accounts (within an appropriation), processed FLIPLs and took people's money, fixed people's pay and allowances in the archaic DFAS system, managed a unit's budget, built budgets based on unit requirements, passed the days financial transactions for requisitions (ZPass) and scoured the system for unliquidated obligations in GFEBS (money we didn't spend but we really spent). End of FY close out takes about 6weeks of your life every year. Certainly work worth doing. These officers were very important to me because vision without resources is hallucination. It is not snapping necks and cashing checks of corporate finance.

If you have an economics degree consider the concept of an FA 59 officer, strategist, and doing something else until you can go to the Career Field Designation Board. Acquisition is another option. Finance is also an option, just understand what you will be doing. Any of the Sustainment branches could use your skills. I know an Economist that has been an Army Engineer for 24 years. Your skills, knowledge, attributes, and desires could be leveraged in any basic branch. You do combat arms and then designate a career field at Captain.

PVT Angelo Velez You are listed as a civilian when you are actually in the Army National Guard. Below is information on changing your status if you so desire.

http://support.rallypoint.com/customer/en/portal/articles/1212628-changing-your-account-status-service-member-veteran-or-retired?b_id=4766