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when you say form do you mean"<form></form>"?
which database is purely your choice.
what are you trying to do with the data collected in the form? (i.e. why do you need to "connect" with a database?). will you be storing it in the database? (many other questions can follow this).
also you'll need some kind of (at least) scripting language to do your data processing (collect data, validate it, store it in the database) if not true backend server coding like java servlets or some other.
what's your goal?