When you say finance, are you referring to something like investment banking? If so, I'm happy to chime in here as I was previously an investment banker.
If so, you should not only think about how you can improve your chances of admission to MBA or MS in Finance, but you also need to start accumulating markers on your resume for investment banking as well. To get from where you are to a job in investment banking, you need to work backwards.
[*] End goal: become a full-time investment banking associate after you get your MBA (I think MBA is more common and I don't know as much about MS Finance but I know both can work)
[*] Before that, you need to first get an internship as an investment banking summer associate between your 1st and 2nd year of bschool. You need to perform well during your summer associate internship to get a returning full-time offer. If you don't do this, you can still recruit for full-time associate positions during your 2nd year of bschool, but your chances of getting a job will be slim to none. 80-90% of the full-time associate positions are filled by returning summer associates who performed well, so you'd be fighting for the remaining 10-20%. And you'd also be competing with other people who have summer associate experience
[*] To get an internship as a summer associate, you need to recruit for it during your 1st year in bschool. There are diversity programs that happen really early (like before you even start your 1st year or right after you start), but otherwise the recruiting process happens in Q4, and you should be done by Jan/Feb timeframe
[*] That means in order to be competitive, you need to have all the relevant experiences accumulated by your first semester in bschool. It's not a lot of time. Which is why I said you should start doing that now, before you even get into bschool
The good thing is, whatever experiences you accumulate now that will help for ibanking, it should also help for bschool. I would do the following:
[*] Get at least 1-2 relevant finance internships/work experiences, more is always better. Relevant meaning something in investment banking (likely small boutique firms), private equity, VC, hedge fund, or even private wealth management. Anything where you have to analyze companies from a financial standpoint. Corporate development could work too.
[*] Learn as much finance as you can - 3 statement and how they relate to each other, valuation methodologies (trading comps, transaction comps, dcf), M&A accretion/dilution, LBO, etc. If you don't know what any of these things mean, don't worry because most people don't. But that's the stuff you'll be tested on from a technical standpoint so you need to learn it.
[*] Polish up your resume and cover letter with these experiences, and format it in a way that bankers like
[*] Participate in some case competitions (ideally ones sponsored by investment banks), especially after you get accepted to a business school
Lastly this is obvious but given how selective investment banks are, they only recruit from the top MBA programs. So make sure you get accepted into a target school.
Hope this helps, feel free to lmk if you have any questions.