Yes, there are statutes of limitations for which you must be aware and you should file immediately if possible. I would file with an address on the invoice at the very least so that you can "toll" the statute if possible. This means that the statute's time limit is delayed since the debtor is avoiding your reasonable attempt to find and serve.
Small claims court is limited to suing defendant's with an address in that county (usually in almost all such courts.)
With regard to liens, you've got a good idea there. That's the one to hit - the property.
This is a link to the Texas Statute regarding Mechanics Liens:
http://www.statutes.legis.state.tx.us/Docs/PR/htm/PR.53.htm
TITLE 5. EXEMPT PROPERTY AND LIENS
SUBTITLE B. LIENS
CHAPTER 53. MECHANIC'S, CONTRACTOR'S, OR MATERIALMAN'S LIEN
Sec. 53.021. PERSONS ENTITLED TO LIEN. (a) A person has a lien if:
(1) the person labors, specially fabricates material, or furnishes labor or materials for construction or repair in this state of:
(A) a house, building, or improvement;
(B) a levee or embankment to be erected for the reclamation of overflow land along a river or creek; or
(C) a railroad; and
(2) the person labors, specially fabricates the material, or furnishes the labor or materials under or by virtue of a contract with the owner or the owner's agent, trustee, receiver, contractor, or subcontractor.
(b) A person who specially fabricates material has a lien even if the material is not delivered.
(c) An architect, engineer, or surveyor who prepares a plan or plat under or by virtue of a written contract with the owner or the owner's agent, trustee, or receiver in connection with the actual or proposed design, construction, or repair of improvements on real property or the location of the boundaries of real property has a lien on the property.
(d) A person who provides labor, plant material, or other supplies for the installation of landscaping for a house, building, or improvement, including the construction of a retention pond, retaining wall, berm, irrigation system, fountain, or other similar installation, under or by virtue of a written contract with the owner or the owner's agent, trustee, or receiver has a lien on the property.
(e) A person who performs labor as part of, or who furnishes labor or materials for, the demolition of a structure on real property under or by virtue of a written contract with the owner of the property or the owner's agent, trustee, receiver, contractor, or subcontractor has a lien on the property.