Can you play Big Fish on them (adventure/hogs/interactive hogs)which brand and version would be best...also play regular adventure games? Also can they be used with DSL?

Big Fish has a number of their games made for iPad.
http://www.bigfishgames.com/mobile-games/ios-games/

DSL has absolutely nothing to do with whether their games work or not. Even their online games work (or don't work) regardless of what type of Internet connection you have (as long as it's sufficient speed). If you have a firewall set up that blocks the Big Fish website, that's a separate issue unrelated to whether it's a DSL or cable connection.

I don't have 'high speed' internet yet...just DSL--do you know if iPads will work with that? I looked online at the Kindle Fire but think read it will only work with high speed...(can't use the Amazon movies or watch because my speed is slow with dsl., However have no prob with Netflix thank goodness!!)

DSL is usually high speed. Of course there are exceptionally low speed DSL (as well as cable) connections that are only about twice the speed of dialup. Check a bandwidth tester to see what your speed is.
www.speedtest.net/
or
http://www.speakeasy.net/speedtest/
and choose the location nearest you for the test.
Or do a Google search for "bandwidth test" and take your pick.

Unless your connection is excrutiatingly slow, there shouldn't be much problem with an iPad.

You can get an iPad with WiFi and it will connect to your wireless setup.
If you get one with Cellular, the Cellular connection won't have anything to do with your current wireless setup, and will probably be a lot slower. However you'll be able to use it anywhere. You'll pay extra for the cellular connection it uses.

I have the slow dsl. is faster than dial up but not high speed. did a speed check several months ago and is the slow dsl. (Windstream had been charging me for High Speed for several months..so had to check to confirm it was slow and then lineman came out and said probably never get it in my area for years...and i only live a few miles from center of town---so still trying to wrangle a way to get our cable provider's high speed(don't have cable anymore..fixed income--and not fixed to my liking!!! hahahaa)
Thanks for taking the time to help...hope you have a nice grilled 'burger or veggie burger today!

And you cannot play Big Fish Games on a Kindle Fire. I know I cannot play them on mine. The Kindle Fire is basically an Android operating system, but with Amazon's Silk on top of it.

To be able to play Big Fish Games on a tablet, you would need to get one with an operating system which is compatible with their games. Some Big Fish Games are ported to the iPad. Or look at Windows tablets which can play ALL Big Fish Games.

As Jenny said, the speed is not important as far as whether they will work or not; it's just a matter of how long a download will take. Once you have a game downloaded, you could play it even if all you had was dial-up.