Something to consider is that there are several states that only recognize permits issued to residents. So your only option for those states is to get your home state permit.
Those states are:
CO, FL, NH, SC, MI, ME, and effectively PA. If you anticipate traveling to any of those states, you need your home state permit.
States that readily issue permits to non-residents and that you don't have to travel there to get the permit are effectively limited to three choices:
FL, UT, AZ.
Utah has a quirky provision in their requirements; since MS recognizes Utah's permit, they won't issue to an MS resident unless you have your home state permit. So that leaves you with the choice of AZ or FL. Idaho's "enhanced" permit is pretty good but you'd have to travel there to take the training and get the permit.
Looking at the maps it looks like Florida permit will get you FL and NM that Arizona won't. FL is kinda expensive but it's also 7 years instead of 5.
What is your rationale for not wanting an MS permit? Has very good recognition, and if you get the MS Enhanced it adds a couple more states as well as better in-state privileges than almost any other non-LE person gets anywhere in the US. Plus you get NICS exemption for firearms transfers in MS.
You say you want a permit that covers more states and lower cost, but MS is already pretty good on coverage.
Arizona is lower cost, but by comparison if you have Arizona by itself vs Mississippi, you would gain NE and DE, and lose CO, MI, SC, PA, NH, ME and FL.
Florida non-resident vs Mississippi resident would be the same other than you'd have Florida.
Interactive map for recognition:
https://www.usacarry.com/concealed_carry_permit_reciprocity_maps.html
Handgunlaw.us is the best reference for details:
http://handgunlaw.us/