If I recently received a second DWI but the last one that I received was 20 years ago, what am I up against?

The prior DWI could still potentially be used against you.  However, considering that your DWI is twenty years ago, they may have a hard time proving it if the fingerprint records are no longer available.  If they can prove the prior, you're looking at a Class A misdemeanor.  If it was a routine DWI, you're probably looking at probation with a DL suspension.  If it was a bad DWI where you almost hit someone, they might consider jail time, but the max time is one year in county jail. 

If the prosecutor cannot prove the prior, then you would be charged with a Class B misdemeanor.  The options noted above would be the same, except shorter time frames.

If you have gone 20 years without any other issues, you have a decent argument for asking for probation.  You will not get a deferred adjudication in Texas though because it's prohibited by state law.  If the facts against you are weak, the prosecutor may consider an alternative charge, like obstruction of a roadway, which carries far fewer penalties. 

You are not required to have an attorney, but it really does help in DWI cases.  This case is "just a misdemeanor" and a lot of people don't stress that much about them.  However, if you plea to this DWI and pick up another one, then the third one will be a felony with a punishment up to ten years in prison.  What to plea to and whether or not to contest the charges are decisions that really should be made with as much information as possible.