This is Samuel and I will discuss this and provide you information in this regard.
First of all, please note that under Texas Election law, you are permitted to register to vote as soon as your entire sentence has been completed. So if you have completed your probation, etc you can vote. You simply need to go to your local Board of Elections and register
Here is the LINK for that Texas Code.
In this code, "qualified voter" means a person who:
(1) is 18 years of age or older;
(2) is a United States citizen;
(3) has not been determined by a final judgment of a court exercising probate jurisdiction to be:
(A) totally mentally incapacitated; or
(B) partially mentally incapacitated without the right to vote;
(4) has not been finally convicted of a felony or, if so convicted, has:
(A) fully discharged the person's sentence, including any term of incarceration, parole, or supervision, or completed a period of probation ordered by any court; or
(B) been pardoned or otherwise released from the resulting disability to vote;
(5) is a resident of this state; and
(6) is a registered voter.
As to not being able to own a firearm and your conviction keeping you from getting work, if you had a Deferred adjudication, you can petition for an expungement and sealing of your arrest records.
If it was not a deferred, then you need to begin with applying for a Pardon from the Governor.