"I want to marry a good guy" is correct. "Get married to" is also a grammatically correct sentence. Which sentence you should use depends on what nuance you want. "I want to marry a good guy" has no particular nuance, but a celebrant (the word for someone who administers marriage ceremonies) also "marries" people, ie. "I married a lovely couple today". If you write it as "I want to get married..." then saying "with" or "to" each have their own nuance. If you say "with" (which is perhaps less technically correct) then there is a feeling that both people getting married are equal. If you say "to" then it has a slight implication that you are less important than the person you are being married to. It is an older word usage which originates from older marriages literally being a woman given to a man, thus married "to". It's the same as "sending to" or "giving to", it slightly objectifies you (turns you into a thing rather than a person). "Get married to" is the more traditional usage, but I would recommend "get married with" as it is gender neutral, and has no historical bias.

We don't say "marry to" or "marry with". You marry a person, so "I want to marry a good guy" is correct. You can use "get married to someone". Be careful of confusion like this. "Married with" seems to only have the meaning of "married, plus...": Married, with children.

I beg to differ, Dorian. There is no implication whatsoever of "inferiority" in "getting married to". "To" is the only correct adjective. "I spoke to the Queen yesterday." "The Queen spoke to me yesterday." "To" does not confer superiority or inferiority. Peachey is right.