An intransit permit and customs broker is required if moving to Belize via Mexico. This only happens at the Free Trade Bridge at the Los Indios border crossing in Hidalgo, between McAllen and Brownsville. This can slow you down, but not a terrible experience. Sometimes you have to wait a few days.
If you are traveling light, with just personal items (like on vacation) you can get a Tourist Permit for you and the car and enter anywhere on the US/MX border. I advise staying on US roads as much as possible and crossing in southern Texas.
With a few dollars (mordidas / bribe) you can pass with your cargo, heading to Belize, using a Tourist Permit (fifteen minute process). Once away from the border, Mexico is great. Always purchase insurance and be drive diligently.
Outside of the border town, you'll find checkpoints on all roads. Your paperwork needs to be in order. I suggest you take a look at the following link and also the related website: Driving in Mexico.