Why doesn't Beatrice want to get married in Much Ado About Nothing? How does she feel about marriage? What type of man would she marry or have...

Sexism was rampant in Elizabethan society.  Women were categorized by extremes, as either virgins or wanton women (promiscuous)--no middle ground.  Women who talked a lot were placed in the wanton category: that's why there are so many interchangeable references to "tongue" and "tails" in Shakespeare's "battle of the sexes" comedies (Much Ado, Taming of the Shrew).

Also, if a woman were not married young--and I mean young (ages 13-16)--she began to garner other titles: "maid," "cold," and "fussy."  I've seen Beatrice played as old as Hero's mother.  So, Beatrice has two strikes against her: she speaks a lot (against men and marriage) and she is older than the ideal woman (Hero).

Look at what Beatrice says when speaking to Benedick: "I had rather hear my dog bark at a crow than a man swear he loves me."  She's very defensive and witty, guarding herself against attack by disparaging the romantic, saccharin version of love.

Look what Benedick says in response:"I would my horse had the speed of your tongue, and so good a continuer."  Though he doesn't call her "wanton," the analogy is clear: she who speaks so much is promiscuous with tongue and tail.

Look what Beatrice says to the Prince: "Good Lord, for alliance! Thus goes every one to the world but I, and I am sunburnt; I may sit in a corner and cry heigh-ho for a husband!"  Notice, she acknowledges her status as "sunburnt" and "in a corner."  She knows she is an outsider and disenfranchised.

Soon after, the men jest: "She cannot endure to hear tell of a husband." And, "O, by no means: she mocks all her wooers out of suit."  And then, "O Lord, my lord, if they were but a week married, they would talk themselves mad."  It is clear: he who marries Beatrice will go crazy with all her nagging.

So, by today's standards, Beatrice is a modern woman: she is not afraid to speak or to defend herself and Hero against men, and she waits until she is middle-age to marry.  Shakespeare makes light of a serious predicament for women in order to change society's view of them--that's the point of comedy.  He recognized the double standards and impossible expectations placed on older, unmarried talkative women.