95' Taurus not starting... what could it be?

[Taurus3.0]

Hi all! I'm new to this forum so let me tell you first that i drive a 95 taurus GL.
has a couple dings not a looker by any means but other than that at 110,000 miles the engine runs rather strong. THe trannie is going and I'm going to be getting that fixed in the near future. Other than the trannie and the most recent problem that has arisen...we'll get into that in a sec I do like my car....

However just recently my car has been stingy in wanting to start. I've got a brand new battery but for some reason when I turn the key NOTHING happens. It Might click once but other than that nothing...just the dummie lights in the dash lighting up, stereo coming on and the fuel pump going... the starter doesn't turn nothing...

Now it might not start for me right now, and i can go outside in 20 minutes and it will just freakishly start right up with no hesitation. MY opinion (and I am by no means an auto mechanic) is that it could be maybe a starter selonoid? or the ignition? has anybody on this forum experienced this same thing with their taurus or other make? I tried starting my car over the last few weeks and it wouldn't start but the other day it fired right up but when I turned it off and turned it back on it wouldn't start? It's really annoying? any idea of the price range to fix? I know it's hard to diagnose over the internet without seeing the car in person but any help, advice or technical answers that you can give would be appreciated! Thanks!

-Steve