If you apply for a citizenship, it won't affect your status, but if you marry your partner who is on F1 and you are on naturalization process, it will surely affect your F-1 holder's status and it won't affect your own naturalization process because F-1 is not an immigrant intent. It is too riksy
There are options:
1) Finish your own naturalization process and your spouse partner should finish college and get her/his own job and get h1. then you can get married. Remember H1 is a dual intent. When s/he gets on H1 status, you can marry your partner and then you can file 1-130 or 131 and then I-485 while you are on naturalization process. It will take a long time for your spouse partner unfortunately because you are not a US citizen yet.
2) After you get citizenship, get married in another country (I am not sure if getting married in usa is a good idea. search for answers in this forum) and file 1-130 or I-131 and then I-485 for your spouse partner if your spouse partner is on H1 and is in usa. or just file to NVC (US embassy or US consulate if your spouse partner is outside usa. It may be a quick process.
3) Get your partner file his/her own H1 and have a employer sponsor her/him for gc. Unfortunately, the process is very painful, too worrisome (economic-layoff, termination, etc), too lengthy, and too costly.
4) File a green card lottery if your partner's birth country is in the list of countries that are eligible. You might get lucky and the process is painless.