The only cage I can think of with ALL horizontal bars is a Hagen Vision cage.
A few members here have them and can tell you more about them.
They don't have a slide out tray at the bottom for cleaning...the cage part detaches from the base for cleaning.
Here is the hagen visions at petco. I know they also have them on ebay for a better price if you want to do a search.
I'm sure others will be around to let you know more about them.
It's very hard to find cages with ALL horizontal bars other than the Hagen.
My guys' cages does not have horizontal bars and they have no problem climbing it. And to make it even easier to climb I just attached ladders here and there on the inside. To be honest they don't use the ladders all that much..they just climb the bars.
I have a cage something like this
The doors are not drawbridge type but I made them in to that type pretty easily. Mine came with 3 platforms but i only use one inside the cage. They LOVE having a good sized platform to play on, and throw foot toys off from inside. Also handy for little plates of veggies.
Here is another that others have and love.http://www.ebay.com/itm/Large-Wrought-Ir...=item3a74951dbb
Again...no horizontal bars and swing type doors.
But plenty of room and dimensions are great as far as length, width to height
If a cage does not come with platform/drawbridge type doors you can always buy platform/shelves that attach very easily in front of the door(s)
Luck with your cage hunt, and welcome to the forum