I have no info concerning the on-time performance of the Sunset Limited #1 into Houston, as I have never been there. Expect for the worst, but hope for the best. When you call Amtrak to buy your tickets, you can ask the agent about the historical on time performance of the trains you have been riding, such as "How's the on-time performance of Train number 1, the Sunset Limited, into Houston?". The agent should, if he or she has such knowledge, tell you the answer, such as "Train #1 is (X hours and) Y minutes early/late into Houston (during the last week)".
As for hotels, give Expedia a try. Enter in the city that you need lodging in, enter in the dates, and hit search. When you do get the search result, look for the ones close to the station, and I prefer to order by price per night, so you see the cheapest ones first at the top. Also, you may want to look for the ones that say "book now, pay later" and/or "Free cancellation", so that you don't have much to lose if you change your mind.
As for dining, give Yelp a try. Enter in "restaurants" in the "Find" textbox, and the city you are looking at in the "Near" textbox.