First-time dental work: 10k budget, no HMO, don’t know where to start

Problem/Goal: Looking to unfuck my years of neglect of my teeth

Never had dental work before. I only got consistent with brushing in starting from my 20s and it doesn't help that I previously used to be a smoker. Now I’ve got black areas, and probably cavities. I also have parts of my teeth chipping, it happened twice this month with small pieces that have white at the outside and black majority on the inside so its really getting me worried which started when I recently started flossing 2 months ago.

Looking for help with:

• Realistic cost for this kind of neglected case
• What procedures I’ll likely need (deep cleaning, fillings, extraction?)
• Where to find a reputable dentist (Google? Facebook? How do I know they’re legit?)
• Would getting an HMO first actually save me money (I have spare income 3k a month would it be practical to maintain it if so)?

I’m totally new to this and could use step-by-step advice, where to go first, what to expect, etc.

Based in Las Piñas, Metro Manila. Local recommendations are a huge help.