Hire a lawyer that specializes in traffic tickets like David Sprecher 713-639-2600. They will know the best way to handle the situation, keeping the expenses to the lowest possible. I would not handle the situation on my own - traffic matters are very specialized (and the traffic lawyers know all the secrets.)
Although I have answered the question to try to help you, you should consult with a lawyer in your area in person on the matter. In addition, my answer does not establish an attorney-client relationship between us.
I agree. I love David Sprecher and he deals with these issues all the time. That you moved out of the country AFTER the ticket and FTA is not a justification though.
You could just contact the court and pay the fines. It will be like $750 total but you can get the warrants to go away and the cases disposed of without an attorney. I'd call David Sprecher first though as he may be able to get rid of one of the charges and negotiate your fines down for under the total amount due without a lawyer. Not sure.