I made a thread like this before but it got archived. I found my certificate from the class, I thought I gave the original to the police and never got it back.

Especially I want to be able to carry in TX since I have family there, but would like to carry as many states as possible too.

Thanks.

Even though a lot of states have cracked down on non-resident carry permit reciprocity, UT and FL are probably still 2 of the best non-resident permits to have.  IIRC, ND class 1 resident permits have the most reciprocal states of any permit but reciprocity drops down to around the same number for non-residents and the drawback is you need to take the certification class/test in ND.

For a MN permit holder,

AZ adds: WY, NM, TX, GA, DE, WV*

UT adds: WA, WY, TX, GA, DE, WV*

FL adds: WY, NM TX, GA, FL, DE, WV*

*Constitutional carry state, so probably moot.

UT will require you to take a class from a UT certified instructor. FL will give you the most overall states and is good for 7 years, but costs slightly more and requires a photo in addition to fingerprints. If you mainly care about TX, AZ is probably the least hassle: $60, fingerprints, good for 5 years

Sources:
https://www.usacarry.com/concealed_carry_permit_reciprocity_maps.html
http://www.handgunlaw.us