Most of your arachnophobia is unjustified, but some of it is not.
I am not a spider squisher. I let almost all of them go on about their business. I guess I have the luxury of saying this because I have a pest control guy so I don't really worry about them coming into the house. As far as outdoor orb spiders or grass spiders, I just thank them for helping keep the other pests down and let them go on about their business.
There are two spiders in Texas that you need to definitely avoid at all costs. First up, are Black Widows. Yes, they are poisonous, and yes, in rare cases they can kill you. You will recognize them by their shiny black bodies and that red hourglass marking (wasn't it nice for nature to put a warning right on the spider). Black Widow actually have a neurotoxin in their venom. That neurotoxin can cause convulsions, cramping, tremors, and all kinds of other symptoms.
Even though Black Widow's are considered to be a bit more dangerous, it's the Brown Recluse spiders that creep me out. Not only are they harder to spot, their venom can cause necrosis at the bite site and eat through your skin and muscle. If you have been fortunate enough to not see what this looks like, then do yourself a favor and keep it that way.
There's not much that can be done about it if you are bitten. Of course, you should see a professional, but all you can really do is wash the area with soap and water, apply antiseptic if possible, and put a cold pack on the site. Those things will help with the pain and possible secondary infections but don't really help with the venom.
Prevention is the best thing you can do when dealing with this terrible Texas twosome of poisonous spiders. Regular visits from a professional bug guy and good pair of gloves will go a long way in the fight against spider bites.
One more item, these are by all means not the only