Okay here is my question, what is some of your favorite baits to throw when it's not a hard bottom. If the bottom composition is muddy what would you throw?

There are quite a few options here and you're going to get a wide variety of responses from all over the country.

I'll say that if the bottom composition is very soft mud and you do not want your presentation to sink into it while you're working it, a drop shot rig is one way to do it effectively.  Virtually any soft plastic bait can be used and the rig does not need to be finesse either.  I've been having quite a bit of success the past two seasons drop shotting a SK Rage Craw.

Good Luck

A-Jay

What time of year?  Spinnerbaits and real shallow diving cranks work well too.  Weightless flukes and senkos, A-Jay mentioned the dropshot, can fish a swimjig, small swimbait.  Most muddy bottom fishing is going to be shallow and up on the bank so any reaction style bait will be good if you're covering water.  Otherwise it's going to be a weightless fluke/Senko or a dropshot rig....at least if it were me.

Unweighted Texas & Wacky rigs or Carolina rigs with only the swivel as the weight or maybe a 1/64-1-32 oz weight.

The same thing .  I use the same lures for soft and hard bottoms . I fish in water so silted in that if you tried to wade in it you would get stuck . I still use weighted T-rigs .

Weightless Texas rigged, black trick worm.

 

That's just being extremely detailed. I know some people are looking for those kind of answers. Could swap it out for a fluke or senko as well. And your favorite color. 

If it is a really soft bottom, I'd probably need a good reason to fish there.   There would have to be some other features to the area.

A mojo rig with a finesse worm works well in these situations.

It's a Senko for me, weightless or wacky rigged.

Some softer lake bottoms are barren.  Other softer lake bottoms are infested with crawdads.  If I had it in my head that a particular soft bottom area was infested with crawdads, I'd spend quite a bit of time in that area.