We here are a friendly bunch and will give much advise. First let me say that you will get many responses here and some may seem unfriendly, but not intentionally.  What you will get from us is honesty.  With that said:
If you are looking to become an abstractor, I would not suggest that you start working for yourself right off the bat.  The online classes DO NOT in any way teach you what you need to know to do this work.  And you will be surprised at the rates for e&o insurance if you haven't done this work for more than 2-3 years.  I'm talking thousands for premiums for insurance.
If you have had companies approach you to do work for them, let them hire you and train you the way you need to be.  This business is not one for the self taught!  Not only does it hurt the industry when those who are self taught get into it, but it can hurt you as well.  By not knowing what you really need to know, you can give yourself a bad name right off the bat if you happen to miss some document or forget something that needs to be checked during your search.
My suggestion and advise to you is to find a company or attorney who is able to train you so you know exactly what you need to know. The good part is you know something about what we do so you won't go into this completely blind about it.
Sorry if that was harsh, just being honest