Depending on your taxing authority, in Texas, the purchase contract and HUD-1 closing statement are all that you should need to defend the value of the home. The appraisal district uses a mass appraisal approach to determining value. That means they aren't looking at your individual circumstances, but a broad brush valuation of an entire neighborhood at one time.
In most Texas jurisidictions, you have a limited amount of time to file the protest, but you do not have to provide the proof with the protest. Just sending a letter to the taxing authority is often adequate enough to put you "into" the protest process. Usually, at some later date, typically starting in June, they will schedule hearings, most often informal for the first one. All you typically have to do is take your purchase contract and the HUD-1 statement and politely tell the appraiser you're meeting with that the value of your home is based on the market value, which you established by purchasing it. Show them the HUD-1 and the purchase contract, and that's pretty much it.
Since you just purchased your home, be sure that next January you don't forget to file for your homestead status. The home may have it now, but that would be based on the prior owner's status as of January 1.
There is one caution in all of this. In Texas, most taxing authorities are taxing you based on the value of your home as of December 31, 2007. If they could establish based on valid data that your home at that time was worth appreciably more than it is now, then you could have a difficult time on your hands. I don't think this is going to be the case, but it's something to verify. For example, let's say you bought your home in April of this year. If they could prove that other similar homes in close proximity to yours sold in late December for 15% more than what you bought your home for, and that your purchase price was impacted by some significant event that occurred in February that negatively impacted your neighborhood and that's why you were able to buy the home so cheap, then you could be in for a nasty fight.
Hope this helps,