Transit Visa

So, researching options for VISAs I noted a Transit visa. It stipulates that it is good for only 5 days, for passing through the country. So, I am looking at rearranging flights to land in Baku, spend a few days in Azerbaijan, then continuing to Sheki and crossing the border into Georgia there.

Anyone have any experience with transit visas and whether that will work for me?

Also, on a slightly different note...lodging. Lodging seems very expensive in Azerbaijan, at least around Baku and Sheki. Does anyone have suggestions for lodging that would be less expensive but still reasonably clean and comfortable? twin room for 2 people.??

Thanks