I do not think you are going to get a ready answer to your questions because maybe these are not two good beginners orchids for SE Texas.

The Beallara, for example has some cool tolerant ancestors that might mean that the plant would struggle to get through summer.

All orchids need some degree of sunlight filtered by something such as shade-cloth and total shade might not be good, especially for the Vanda.

Sorry that this is not much help, try to find some cultivation notes on the net that relate to the climate where you live or contact some of the local orchid societies for further help.

Don't pay any attention to the previous post, Arthur is just an old grump. Both these orchids will do fine for you provided you meet their needs, which are different. Vanda needs to be grown in full sun esp.during the winter months. It also likes heat and humidity, so whilst it will do OK out of doors in summer in Texas, with a bit of extra watering, it will need indoor protection during the winter. I would use a hose to water as it likes to be grown without any compost. Yes that's right. In winter it will need heat and very good light to keep it going. Well grown they can flower several times a year. Origin: SE Asia.
Beallara is a hybrid genus and grows fine for me in Brazil which is fairly warm most of the time. It needs a lot more shade than Vanda, however, and probably needs greenhouse treatment where you live as it does not like big seasonal variations of temperature/humidity or water, though it can be drier in winter. Keep it within a temp. range 50-80 all year round if you can and watch out for pests on the backs of the rather thin leaves esp. if humidity is low. Hybrid: but most of the parents are from upland areas of tropical S America.
Good luck. - Ian.

Do pay attention to my post. How can anyone in Australia tell you in specific terms how to grow an orchid in SE Texas? Read up on culture and seek advice from the local orchid society(s).

Ian, this is a discussions page. Rudeness has no place here.

I've been doing a lot of research over the past few days and have found a local orchid society. They have care instructions for different genera of orchids tailored to the local climate. Vanda Alliance orchids (it turns out mine is actually an Ascocenda) are good choices here, but need to be brought indoors during the winter months. They didn't have any info on the care of Oncidium Alliance orchids in SE Texas though.