In a 10 gallon I don't think both a UTH and CHE/Lamp are necessary. One or the other, and I'd lean towards the CHE.
The UTH isn't going to do anything for the cool side, I've experimented extensively with this and found that unless the ambient room temp is a steady 77F (and that's a minimum) the UTH on its own is never going to cut it.
A CHE on the other hand will be able to get the warm side to 90 and the cool to 80, and comfortably so. Plus you'll only need one thermostat.
I prefer CHE for BPs for a few reasons;
1) Light stresses them out. They like darkness.
2) The light only emits heat when its on. Do you want a light shining at 2:30 AM?
3) A switching thermostat (like a Jumpstart) is either on or off, no in between. All this on/off/on/off shortens the life of an incandescent bulbs.
They do sell red lights that mitigate 1 and 2, but not 3.
CHEs last longer than bulbs under all circumstances. I think the on/off nature of Jumpstarts shortens their life as well, but they last so long that this is less of an issue. A CHE is more expensive though and will tend to dry out the environment, making humidity an issue. I now use Radiant heat panels myself (most expensive option).
Finally, don't take my word for it. Everybody has their own way of doing things and lots of methods can be made to work perfectly well. There are many experienced keepers on this forum who will gladly give you advice that may be better than mine. Read, learn, absorb, and devise a method that will best suit your situation and goals.