Would all men think you are trashy if you had tattoos? Not at all. Would some men think you are trashy? Yes they would, and there's nothing you can do about it.
Some men have a strict "I don't date women with visible ink" policy. Other men have an even more restrictive "I don't date women with any kind of ink anywhere on their body" policy. These types of guys may be turned off by tattoos, or don't like how they look, or even have an issue with what body art represents. So if you get a tattoo, you'll eliminate your chances with those men.
Let me temper that dire warning somewhat by telling you that the majority of men don't worry too much about whether or not the women they're seeing has any ink. For every one guy that will cross you off the list for tattoos, four guys will appreciate you ink and all.
Keeping this in mind, my advice is this - get as many or as few tattoos as you want. If you long to be covered head to toe, make it happen. If you want to keep your skin unadorned, do that instead. Do what makes you the most happy and your life will adjust accordingly.