There are so many different definitions of "psych music" these days that I think the best route is to try a few different comps to try to determine what definition is your cup of tea.
One school is "Garage Psych" that is typically American and is represented by bands like The Chocolate Watchband, Electric Prunes, Elevators, etc. Evolved directly from "Garage Punk" these bands smoked some dope, dropped some acid and took the early Rolling Stones/Beatles sounds to the next level.
Then there's West Coast Psych and because of it's popularity at the time, this is considered more "mainstream" with bands like Jefferson Airplane, Byrds, Doors, CJ & Fish and even Janis & Jimi.
60's Avant Garde or Freak Out psych includes bands like The Godz, Cro-Magnon, Silver Apples, 50 Foot Hose, etc. Probably all more popular today than back in the day.
Pop Psych or "Sunshine Pop" is another genre that has gotten a lot of attention with LP's like JK & Co., Millenium, etc.
Folk Psych is a whole nother bag and while there are a lot of LP's defined as such, most aren't. Linda Perhacs is the epitome of female folk psych and Perry Leopold the male counterpart.
Bands like Ash Ra Tempel, Brainticket, etc. cover the "space psych" or prog/psych genres and is mostly a Euro style.
Then there is Hard Rock/Psych, Rural Psych, Modern psych, and about 10 other sub-categories. People like Zappa and Captain Beefhart fit in there somewhere too.
All I'm saying is 1) Don't be turned off to Psych in general if you hear one of these genres and it's not your thang....and....2) Find out what style is your fave and then you can dig deeper into that genre as I've really only mentioned major label artists above and the MAJORITY of psych, as documented at the Lysergia website is private press underground fare.
Rich