You have received some wonderful advice so far. When it comes to insuring your things you don't want to scrimp. Think replacement value. How much will it cost to replace everything, tv's, blueray players, videos, video games, videos game systems, sofas, chairs, tables, lamps, curtains, towels, sheets, clothes, soap dish, curling iron, clothes iron, children's toys, ironing board, etc. As you can see this list can get exhaustive, also include the cost for possibly having to live or stay at a hotel while you wait for your place or a new place.
The actual costs for renter's insurance is affordable. When I rented I also had a $1,500,000.00 liability policy which was also affordable. I think I paid something like $65 a month. Which as great I thought especially for how much coverage I had. Insurance in my New Jersey is probably higher than what you could expect to pay in Texas but getting quotes is free so get your quotes and then make an informed decision.