It is unlikely you will find a thermostat that is appropriate at home depot. I personally would suggest a herpstat or any other proportional t-stat as being the most trouble free. The downside is the price is also quite high as they are all about 105$ or more.

The other types are on/off they will work as well often needing a bit more tinkering but glass tanks are quite well suited to them. Hydrofarm (look on amazon) is a viable one it is about 40$ The others commonly used are Johnsons and ranco but the cost savings there is quite low as they are in the 70-80$ range and to me I'd just bite the bullet and buy better at that point. All of these need to be carefully checks as the temperature you set on them is often not as accurate as many would like.

No body has identical set ups and nobody has the same problems. You may need the heat lamp help hold your cool end temps. They should not be dropping below 75ºF. do what you need to to hold that.

What are your temps now? Hot spot inside the hot hide, and cool end inside the hide, ambient air temps dangled probe in the mid point of the tank and when the probe is directly on the glass over the UTH. If your glass is not getting above 92ºF you are ok for the time being. If it is hotter then I'd try to order a t-stat asap.

It is never a good idea to have anything in the enclosure that is over 94º snakes systems are tuned for average temps not spot temps a snake will burn a part of it self to get its core temps up.