First of all welcome to the T&TH forum. I know you'll enjoy it here. There are so many good folks who are very helpful.
Mossberg can give you a lot of gun for the money. I am not a big fan of 3.5" guns and only recommend them to folks who intend to shoot steel shot for waterfowl and want/need the extra capacity of those shells for the larger steel shot. If that is the case, you'll also need a longer barrel, 28" is best in my experience, to get a full burn with the slower burning powders used in steel shot loads.
Whether you choose the 835 or the 535, I'd sure recommend that you consider a longer barrel than either the 20" or 24" that you've mentioned. While it's certainly possible for a barrel of that length to pattern very well (and no doubt someone will post a reply who has one that does) your odds are greatly increased with a somewhat longer barrel, at least 26".
I've had hundreds of folks who have contacted me through my site about poor patterns with very short barrels. Since Mossberg sells so many shotguns and many (turkey models) in the last few years have been offered with short barrels, most of these complaints have been about them.
I should add that some of the best patterns I've ever seen have been from Mossberg 835/935 shotguns with 28" barrels. The shorter ones are a real challenge.
After several years of working with 835/935 shooters, I also wrote an article specifically for those guns and you can read it at http://allaboutshooting.com/article_info.php?articles_id=242
it's certainly not rocket science but it has helped literally hundreds of shooters (not just Mossberg) get better performance from their guns.
I think you'll find that there is very little difference in maneuverability with any of the barrel lengths and the extra length will help with patterns and also help just a bit with recoil reduction and give you less muzzle whip.
I'd also recommend that you consider shooting 3" turkey shells in your gun, regardless of the model. Generally they pattern better, they cost less and they deliver much less recoil.
Lastly, in my experience the 835/935 guns get the best performance with a turkey choke with a .670 exit diameter. I use and recommend the SSX with that gun. I also shoot and recommend the SSX with an exit diameter of .643 with the 535. Those chokes have the best internal geometry, in my experience of any turkey chokes on the market, they are rated for all lead and "hard" shot and are very reasonably priced, especially for the quality.
If I can be of any help whatsover, please just let me know and I'll do all I can to be of assistance.