You are a wise person to be thinking about possible problems BEFORE you get married!
You need to make sure that you both have wills in place in order to protect yourselves.
Please talk to an attorney that handles wills and probate.
For example, if your spouse does not have a will in the State of Texas and you purchase a home together, you could end up owning a home with his minor children from his prior marriage. I'm sure that this is not something that you would enjoy doing since you would then have to interact with their mother!
Also, if your spouse dies, then his/her child support becomes an obligation of his/her estate. Yes, that means that his ex-spouse would intervene in the probate of the estate. You and any children that you have with your deceased spouse would be "punished" since the older children would probably have a superior interest in the assets of his estate.
You should also talk to an attorney that handles family law matters about possible problems if the parent ever gets behind in his or her child support obligations in the future. He or she might be current in his (or her) child support NOW but if he/she ever falls behind it could definately impact any property (or bank accounts) that you might purchase together in the future.
What would I do?
Here are just a few things that come to mind...
You probably don't want to keep all of your finances separate.
So no joint bank accounts.
File your taxes separate.
Consider signing prenup (and post nup.) legal paperwork that had been prepared by a family law attorney.
Review your wills every 5 years.
Review your finances every 5 years.
Put assets in your name only.
Run your credit and your spouse's credit annually.
In summary, you might want to just together and not marry.
Remember, if you have any children with this person, they take a "back seat" to the children that are already alive. The Courts will always "favor" the older children. Why? Because you knew that these children were alive and their parent had a legal obligation to support them. The judicial system will have no sympathy for you or the younger children.