Lot of questions packed into a small space. The instructions should appear on the reverse side of the citation. Those instructions need to be followed to the letter. There is a strict time limit for pleading not guilty and requesting a hearing; make sure you do it in time. There is likely a requirement that you post money at the time you request the hearing as surety. If you will you get it back, if you lose it is applied to fines and costs. You do not have to have a lawyer represent you aft the hearing. I think is a good idea from the standpoint of maximizing your chances of success, but as you've already pointed out the cost of counsel may exceed the amount of the fine. Remember there may be negative consequences with respect to your cost for insurance because of this; so factor that in to the decision about hiring an attorney. The last part of your question regarding points will have to be answered by a lawyer licensed in AZ and familiar with its point system. Good luck.
Points are assessed based on a schedule from the MVD on a conviction for speeding, so if there is a conviction for speeding normally points would be assessed against your license. Whether this information will follow you depends on the state, but most times it follows you.
With respect to a resolution it is possible that you could qualify to take a traffic class in lieu of a conviction. You must contact the court to make these arrangements if you qualify and then follow through with completing the class. The classes, which can be online, normally costs about as much as the ticket ($200 - $250). The classes if you complete them do not result in points against your driving record (license). You can only complete the classes to avoid a finding of responsible for the ticket once every 24 months and the classes only apply to civil traffic violations (which speeding tickets normally are).
This information is provided for general informational purposes and is not intended as legal advice. An attorney licensed in your jurisdiction can answer questions specific to your specific fact situation and provide you appropriate advice as necessary based on the specific facts of your matter and the jurisdiction in which you reside. If you are in Arizona and interested in discussing your matter further I can be reached at: (480) 838-9000 Mark D. Fullerton, P.C. 1839 S. Alma School Road, Suite 275 Mesa, Arizona 85210