I'm in the market for a new or new to me saddle and I'm having a hard time finding something that checks all my boxes for a reasonable price. 

I want a deep seat, forward hung stirrups, and prefer actual leather as to the synthetic since when I purchase a saddle it's meant to be used for a long time and will be the only saddle I have to ride in. 

Doesn't seem like it would be that difficult to find but...

I am finding that most of my preferences are saddles with flex trees. I am not really sure how I feel about that, I have only ever owned wood tree saddles with the occasional treeless that I would end up selling after a few months. 

Thoughts on flex trees? The good, bad and the ugly! 

Try a Debra Sibley, it has everything you've mentioned and I love mine.  It rides like a treed saddle and doesn't fold up like a treeless.  The down side is the leather isn't the best quality.

If you can I would borrow a flex tree from someone if possible are buy a used flex tree and try it befor you spend money on a new one, the flex trees do have a different feel for you and the horse I know some horses have to take time in getting use to some flex trees. 

I have ridden in flextrees for years.  The only one I would suggest staying away from are the Reinsmann.  I bought a beautiful one brand new made by them and it was JUNK!  I have had my current ones for a few years now and they are FABULOUS and well made.  I got them from Felecia Carlton (Horse Tack World) and they are made by Circle Y.  I LOVE them!

Can you tell me what feels different about them as a rider? I have heard people say they feel like they "bounce" in them. Thanks! 

I've had two national saddle reps tell me they will not ride flex trees. I obviously can't say which two, but both companies sell tons of flex trees. I'm a big girl so I'm looking for very minimal movement. 

Flex trees and sports saddles are two different things.  I have had several "flex tree" saddles and they ride like an ordinary hard tree saddle. A well known saddle maker told me the only difference is the wood is a little softer type  of wood so has a very slight give in it......it can barely flex a little.  IMO that makes them more likely to get a twist in them or break.  I have broke one and twisted 2 on a really big stout horse that I also used a snug back girth on.  I think using the back girth put too much strain on them during a turn. That said, I do not like them.  I have one but I'm not happy about it.  I also have a sports saddle and 1 horse hates it, a couple more love it.  They do tend to put more pressure in a smaller area on the horses back (where you are sitting) vs the solid trees seem to be putting more pressure on the withers and shoulders.....even when the "fit".  Overall conclusion:  Try them all and use what your horse likes.  Use good pads. 

A flex tree does exactly what it says.  It flexes, Sort of.  However, that also means when you sit on it, it flexes directly down onto the horses spine.  Think sitting in a tire swing.  It flexes around your bottom in order to hold you on the swing.   Well, a flex tree saddle does the same thing.  It might flex "open" to hopefully fit the horse, but it also flexes from the pressures put on it from the rider. 

Here's a short 8 minute video showing that flex trees aren't all they're cracked up to be. 

https://www.youtube.com/watch?v=HKhponXAt6I

I have mixed feelings about them. Depends on the horse for and the type of saddle. I have two circle y flextree trail saddles I use on our friesians and love them. That being said, I bought a circle y flextree barrel saddle for my qh mare and hated it. It made her back sore and sat me way too far forward with my feet behind me. I had to sell it and lost a fair chunk of what I paid for it.

I would go with a tree less before I went flex tree and I have had both.