Reddit mentions of adidas Golf Men's Climacool 3 Stripes Polo Shirt, Black/White/Vista Grey, Medium

Alright...
Ol' Florida boy here, so I'm aware of the pain.

First, you need a good offset umbrella. Get the offset, so that the pole isn't in the middle of everything. Deck chairs are up to you. Everyone has their own comfort level for chairs.

I recommend a big ass fan that you can put far away, and that can move air across your whole area. If you're so inclined, a fan mist kit can help a lot too. This may or may not be convenient (or necessary) for you, depending on your setup.

I'm an outdoorsy kinda guy, and I'd rather hang out outside all day than sit inside. As such, I recommend Adidas Climacool Shirts. They make other styles than the golf/polo shirt type, but the fabric is amazing in the heat.

Keeping with the staying outdoors all day theme, I always recommend a good hat to keep you cool. Hats are, of course, a personal preference, but anything with a nice wide brim, and plenty of ventilation is great.

Now, a cooler isn't necessarily required, however, if you're the cooler type, then you can't go wrong with a stainless steel patio cooler. If that's a little outside your budget, maybe go for a plastic one. Those Marine Ultra ones can hold ice for days without a problem.

If you've got the cooler, but you're more of a mini keg kinda guy, you could get a jockey box kit to slap up in a cooler. If you had a decent sized cooler, then you could still keep some sodas or water in there.

Now, I don't know about you, but when I'm chillaxin' out by the bbq, I like to get down with some tunes. You can get some outdoor radio setups for pretty cheap. We always managed to hide speakers under the roof overhang, and this seems geared towards it right out of the box.

Now, I'm not much of a TV guy, but if you're hanging out with the friends and family, especially in the autumn, someone's gonna demand to watch the football game. I have a crappy little 32" TV that I like to pull out and connect to the stereo, so we can put the game(s) on. Get one you like. That was just the first one I found for under $200. The one I've got is an older model from Sharp, and has a matte finish on the screen, so the viewing angle is very wide, and it's pretty easy to see, so long as there's a little shade over it. Also, $200 isn't a critical loss of cash if it gets rained on. Though in the 5 or so years I've been pulling the TV, it has never gotten wet enough to be a problem. (It rains nearly every afternoon during the summer where I'm from in FL).

Those are just some ideas, and not a comprehensive list. I didn't mention anything about mosquito control, as I don't think I've ever heard anyone refer to Texas as "swampy".