I worked for an endodontist (root canal specialist) for six years and I also have experience working in a general dental office. First piece of advice: Get a second opinion from another general dentist. Second piece of advice: Have an endodontist do the root canals. Endodontists routinely redo the ones done by general dentists, particularly on molars, because they're difficult without the specialized equipment.
The teeth that you need root canals on will also need crowns. (Aside from the two that you already have crowns on, of course.) Your dentist should have given you a tiered treatment plan, specifying what's most urgent. Without knowing if you're having pain or if anything is infected, here's what I'd recommend (I'm assuming no pain/acute infection and also going on the assumption that a second dentist will give you the same treatment plan, which is a big if.)
1. Go and get the fillings done on your front teeth (10 is the one on top and 25 and 26 are on the bottom) and that bicuspid (21) on the lower left. Those should be fairly inexpensive and mostly covered by insurance.
2. Next priority is the root canal (and subsequent crown) on tooth #20 (also a bicuspid on the lower left).
3. Next priority are the root canals on 3 (upper right first molar) and 19 (lower left first molar). Those will need fillings in the crowns afterward.
4. Last priority are the root canals on 15 and 2. Those are the last upper molars in your mouth (assuming you've had your wisdom teeth out) and if you lose those, so be it. You'll still have enough teeth to chew and smile.
I don't know about the issue with the implant; if it's salvageable, then put that up higher in the priority list. If not, just get it taken out and in that case, #19, which is directly under it, can also go down on the priority list. Obviously if anything is very painful or acutely infected, that tooth moves up on the priority list to be dealt with as either a root canal or an extraction.
As far as paying for the work, getting your own insurance is one good plan. If you have decent credit, you could apply for Care Credit (
www.carecredit.com). It's a medical/dental credit card that can also be used at the veterinarian, eye doctors, and a few other places.
Good luck! Dental work is expensive.