You didn't mention what style of hunting you'd be doing... I've done a ton of axis hunting all over west Texas and the hill country region in every way imaginable, from sitting blinds with a bow to stalking with a handgun/rifle, etc. etc. If you going to be out beating the brush, you will need sturdy leather boots and gaiters aren't a bad idea. You can stalk in shorts just like it's done in Africa or wear some light cotton camo pants. The camo cooling fishing shirts or something similar work well, but so does light cotton, or the light Sitka type shirts. I always have a good hat to guard off the sun and drab looking sunglasses that aren't too bright to the game in the sunlight. Some camo patterns blend better than others in that country, but it will depend a lot on the amount of rain the area has been getting. It can be pretty green or downright brown, depending on ground moisture. Movement will be what gives you away most of the time, and in good axis country there will usually be a whole lot of eyes looking out for danger. Axis are very wary critters, even on lightly pressured ground. Put a little pressure on them and it can be a tough animal to stalk, although we routinely stalk them with archery gear with some success.
June and July are great months to hunt axis. The majority of bucks will be hard horned and rutting hard. June may or may not see many 100 degree days, but July surely will. When I'm going to be walking a lot, I head out with one cold water bottle and one that's at least mostly frozen in my pocket or light pack.
Be ready to dump the guts quickly and get the meat cooled down asap, and a walk in cooler that you can work on the butchering inside of is perfect. If you are fully guided you may have someone doing this for you. Axis meat may be the finest venison you've ever had, and you don't want to waste a morsel of it. I've eaten just about everything this continent and Africa have to offer, and axis is as good as any game meat, if not the best in most folk's opinion.
Shoot axis deer at least a little bit more forward that you do whitetail. Directly through the shoulders on a broadside shot is a good rule of thumb. Tight behind the shoulder will work, but straight through the shoulders is better. They are far from bullet and arrow proof, but I have seen some hardy, big bodied bucks go mysteriously unfound by the hunter, sometimes with video proof of a very well placed shot. I know it makes no sense, but it sometimes happens. Just bear down and make every shot count. Big mature axis bucks are amazing big game animals, and when you see a good one rutting and strutting on the hoof, you will be mighty impressed.
Lastly, the rutting bucks make a roar kind of like a bull elk bugles. No, they don't sound the same, but they mean the same thing. He will roar as he roams in search of a receptive doe, and he will roar when he's just hanging out with a feeding group. Axis are grazers, not browsers like whitetail deer, and they often travel along in a sizeable herd while grazing on grass like cattle do. The bucks will commonly roar in a 3-call sequence, and you will find yourself making estimates on the size/age of the sounding buck, but you will often be surprised to see what he really looks like. If you have the chance, hunt them by getting the wind in your face and slipping very slowly and quietly towards the animal, using any and all cover to hide your approach. This is about as much fun as you can have with your clothes on!
Good Luck and keep us posted.
Jeff