@beckyqtoo

In the panhandle, I would wait until spring. Probably late March would be ideal. Now is probably a great time to do any soil amendments, grade changes or preliminary hardscaping that you have planned before the plants go in the ground.

For palms, Florida has 11 (or 12, depending on your scientific persuation) native species. I've added a + next to the ones I would consider planting there:

Acoelorrhaphe wrightii (+): The canes tend to freeze back below 15F, but they can come back from the roots.

Coccothrinax argentata

Leucothrinax morrissii

Pseudophoenix sargentii

Rhapidophyllum hystrix (+): Small shrubby palm that grows well as an understory palm. This palm is so hardy it is grown in NY an NJ in some areas.

Roystonea regia

Sabal etonia (+): Probably not planted as often as it should be. Small, shrubby palm with good cold hardiness. (Sabal miamiensis is now considered botanically part of Sabal etonia)

Sabal minor (+): There are a lot of different varieties. The 'Cherokee' and 'McCurtain' varieties are unbelievably cold hardy, with the Cherokee variety being native to a zone 7b area. The Sabal Louisiana variety tends to get a small trunk. Emerald Isle is a variety that gets a little larger than some of the other very hardy varieties. If you want some locally grown dwarfs, Blountstown Dwarf is a very popular small variety.

Sabal palmetto (+): You'll probably want the booted variety (most common). You can plant epiphytes in the boots if you want a more decorative planting.

Serenoa repens (+): In particular, the silver variety is very attractive. At full size, they make a great 6-10 foot high border.

Thrinax radiata

Some hardy non-natives that should do well there:

Butia odorata: The typical Jelly Palm sold in home improvement stores and nurseries.

Chamaerops humilis: The silver/blue variety (Chamaerops humilis 'argentea') is especially attractive. Plant them slightly elevated and in a well drained area for best growth.

Sabal mexicana: A close relative of our native Sabal palmetto, but with larger seeds.

x Butyagrus nabonnandii (Mule Palm): A cross between Butia odorata and Syagrus romanzoffiana that is often sold in home improvement centers. Typically cold hardy down into the teens and sterile, meaning no volunteer seedlings.