Is it legal to refuse to sell a home to a sex offender?

No, as sex offenders are not a protected class under the Fair Housing Laws.

This will be the first time that either one of us will be going through the home rental process. What are some things that we should know when we start the process of looking for a place to live? What do people look for when the decide on whom they trust to rent their property to?

Rental homes go quickly, so in addition to the good advice you have received, I would say that when you start to look is important. For example, if you need to move by Feb 1, you would want to be looking around the first of January. Anything you see on the market now, will most likely be gone by then and landlords don't want a house to be vacant any longer than it has to be, Also, more homes are listed around the first of the month as previous tenants move out at the end of the month and homes become available. Good luck!

Im looking for a small home/condo/townhome with owner financing in The Woodlands. I have 30.000 down payment.

Owner financing can be a good deal for the home owner but isn't always great for you as a buyer. You are likely going to need 20% or more down and interest rates are considerably higher than what you would pay for a FHA loan with a shorter loan payoff resulting in large monthly payments.Most home buyers that I have worked with have considered owner finance due to lower credit scores that are preventing them from being able to get an FHA loan. Another option would be to rent a home for the time being while you work on repairing your credit (assuming that is the issue) so you can secure an FHA loan at some point in the future. In the long run that may be a better option for you....