In Texas, in terms of who pays for a residential service contract (RSC, aka home warranty), the act of purchasing one is ALWAYS executed by the buyer - either through an independent act by the buyer after closing, or with the title company ordering one for them during the closing as a courtesy upon instructions by the buyer as detailed in the contract. If you are able to negotiate for the seller to contribute an amount equal to the total cost of whatever you as the buyer purchases, then great. Many buyers ask for this "goodie" - some get it, others don't. It just depends on how important it is to you.
Regarding RSC's in general, the question you need to ask yourself is simple - given the age and condition of the property that you are considering buying, what is the likelihood that a major mechanical component will break down? And if it does, will it cause a significant financial hardship on you if you do not have an RSC in place? Given that you are considering a 3 year old home, the chances of the A/C or the hot water heater blowing up are probably fairly small, especially if the previous homeowner has undertaken minimal maintenance. If you DO decide to purchase an RSC, know that if something like the A/C breaks down, it probably won't cover the entire cost of the repair. If you need an entirely new A/C, the total cost might be $6,000 or $7,000 - and the home warranty might cover $4,000 of the expense. Without going into minutiae, just know that there are "related costs" that are not covered in an RSC - hence the difference. But having a policy in place would save you several thousand bucks, so it's not to be sneezed at.