In the state of Texas, you don't have to register your kayak in most cases. If it has a motor, trolling or otherwise yes, but in most cases no. Laws are different in each state so make sure you check them out carefully before venturing out. Here is how it reads in Texas:
The following vessels when on Texas public water are required to have current registration, including when docked, moored, or stored.
That is great news but slow down for a second and let's really look at this. Just because you don't have to register your boat (as long as you meet the above criteria) doesn't mean you can stroll down to Mariner-Sails and pick a boat and a paddle and be on the lake before sunset. There are some other things to look at within the laws.
Just to get on the water you need to read this:
All vessels, including canoes and kayaks, must be equipped with one Type I, II, III or V wearable PFD for each person on board. A Type V PFD is acceptable only if used in accordance with the specific instructions on the label of the device.
Need some help picking one out? Visit a kayak dealer and try some on. For more info, check out this post here. And if you want a direct link to a recommended manufacturer? You should check out NRS or Stohlquist. PFDs are what they do.
If you are going to paddle at night:
Remember that you must carry one bright white light that can be exhibited in time to prevent a collision. It is recommended that you carry a lantern, flashlight, or other attached white light that will be visible from 360 degrees. Regulations state that canoes, kayaks, and all other manually driven vessels may exhibit sidelights and a sternlight, and shall exhibit at least one bright light, lantern, or flashlight from sunset to sunrise when not at dock.
Need some help? For the absolute best you need to look at the YakAttack VisiCarbon Pro Light. You can find it here with a Mighty Mount (others are available). It also has a hi-vis flag so people will see you during the day as well.
A general warning to have your safety items:
Operating Vessels without Required Equipment is Prohibited - No person may operate or give permission for the operation of a vessel that is not provided with the required safety equipment. An operator may not permit a person under the age of 13 to be on board the vessel while the vessel is underway if the person is not wearing a USCG approved wearable PFD. Marine enforcement officers regularly perform vessel safety checks to ensure the safety of boat owners and passengers.
One more thing you will need by law:
Any vessel less than 12 meters in length (39.4 ft.) is required to carry a whistle or horn, or some other means to make an efficient sound to signal intentions and position in periods of reduced visibility.
As you are thinking about total purchase price, a weekend trip down the Brazos, Guad or just a play day at the lake, make sure you have a PFD (life jacket), whistle, and if paddling at night, a 360 light.
Stay safe, not only will it save you money but it might save your life!