If one met a very nice Jewish girl and would like to marry her but was told she can't marry a non-Jew, and decided that one wants to convert to stay with her, would that be acceptable? And whole heartedly accepted the commandments with intention to believe on the same level as her.
Masechet Gerim (1:7) rules that conversion in order to marry a Jew/ess is invalid:
כל המתגיר משום אשה, משום אהבה, משום יראה: אין זה גר.
The Talmud (BT, Yeb. 24b) ostensibly maintains the same, i.e. conversion for marriage is prohibited.
However, halachists, particularly of recent (R. Grodzinski, R. Uziel, R. Waldenberg, R. Yosef and particularly R. Haim Amsalem who wrote extensively on this matter in his books Zera Yisroel), have demonstrated that such is not a bold and concrete rule and have ruled leniently accepting and affirming such a conversion when the non-Jew demonstrates a genuine intent* to be a religiously observant Jew. See this essay for exact sources.
*For a suggested determinant, see Yabia Omer vol. 2 EH §3. He suggests that the convert first be rejected and subsequent, voluntary conversion be sanctioned.
Thank you for the question - which you ask during the week where we read the Torah portion of Jacob being willing to work seven years to marry the woman he loves, Rachel !
Yes, one should convert for love - for love of Hashem (God), the Jewish people and the Torah of Israel. Judaism is a demanding religion, i.e., there are many commandments (obligations) to learn about, it requires a real change in day-to-day behavior and there are some demands specific to the conversion process (e.g., learning about Judaism, living in a Jewish community, circumcision for a male, passing an exam in front of multiple rabbis).
Wanting to marry a Jew can be a trigger for such a process but it requires thoughtful thinking and a multi-year process for most individuals. It cannot be the only reason.
Should you be interested to take things forward, you should find a local rabbi who is willing to explain what the process entails and accompany you along.
The following articles might prove helpful to understand better what conversion entails