#1 priority.. make sure it seals really well.. from the pictures it doesnt look like it has any sort of material on the doors/frame that would help keep RH in/out.. you want a sealed/constant RH environment for cigars..
#2.. careful about using that cooling unit.. you DO NOT want to be running a compressor based cooling unit.. you want thermoelectric.. Im guessing that unit is a compressor..
All that said.. this looks like a seriously fun project..
you can probably seal that thing up tight as a drum for less than $20.. weather strip around the frame where the doors touch should do the trick.. then use an odorless caulk/sealant on all the seams internally.. and you should be squared away..
Get lots of spanish cedar in there... Start out with empty cigar boxes or whatever you can get for free/cheap from your local B&M and HERF buddies.. but you dont want a whole lot of open air/space inside.. unless youve got a couple of thousand sticks on hand already.. with something that massive youre probably going to have some open space for a while.. consider ordering some custom trays/drawers from Forest...
In TX youre probably going to want a cooling unit of some sort.. unless you have a place in the house that stays between 65-70 all the time that you plan on putting the cabinet in?
youre going to want to think about RH media as well.. some people swear by beads.. others by KL.. others by active humidification.. etc.. its really a matter of preference... My cabinet is about 1/2 the size of your project.. I use a combination of active (Oasis XL), KL, and a handful of bovedas.. its not the most conventional approach.. but it works well for me.. and is extremely low maintenance..
Youre probably going to want a couple of fans in there as well.. thats a lot of space to keep your RH balanced in.. if you go with active humidification like the Oasis XL.. it has a fan built into it.. If you can find them, a lot of guys like the old Oust Fans (battery operated).. some people go with computer fans.. again.. much of this is preference.. but Im guessing you are going to see a significant difference in RH at the top of that box and what you get at the bottom (my cabinet is about 6' tall.. before I put a fan in mine there could be as much as a 5% variation between the bottom (where the Oasis is) and the top (KL and a couple of bovedas)... Now that Ive got an additional fan in there.. top to bottom deviation is never more than 1% (usually its spot on)..
Good luck with your project..
I had a lot of fun building mine out earlier this year.. Im betting youll have a lot of fun with yours as well..