I was referred to RAMP under similar circumstances, so I'll tell you my experience and hopefully you'll find it helpful. I got a DUI prior to becoming a nurse, prior to applying to nursing school even. RAMP starts off with an initial "phone interview" where you basically have to detail any and all substances you've ever used/abused, any mental health issues you've experienced, etc. Followed by you signing up for mandatory "support group" meetings and submitting to random drug testing. IIRC they tell you you'll be evaluated by one of their therapists after you have been in the program with x number of clean drug tests. They tell you that if the therapist recommends you receive treatment, you'll be offered a 5-year contract to stay in RAMP. If you accept, you'll receive your license, if you don't, the board denies your licensure, but in reality, it seems to just depend on the whim of whichever person you get assigned as your case manager. My evaluator told me she was recommending I be discharged since I had one DUI years ago and no history of substance abuse issues or other deliquency. RAMP told me after reviewing her input I was being offered a two-year contract for "mental health" because I had honestly answered that I was taking Prozac prescribed by my doctor for depression, and this meant I was as unsafe to practice an in need of monitoring as someone in active addiction who had been caught diverting drugs, apparently. It doesn't make any sense. There were people in my "orientation" support group with the exact same charge (DUI prior to licensure) who were discharged and granted their licenses and allowed to practice freely. But like I said, it seems to depend on the whims of the RAMP employees who gets "treatment" and who doesn't.
As far as there being "tiers," unofficially as RAMP doesn't outright say this, it seems that if you have substance abuse issues or have otherwise misused your nursing license (for example, I've seen people who got 5 years for lying about the dates of their CEUs) you get offered a 5-year contract. If you can "pin" the issue that got you into trouble with the board on any sort of mental health issue, you may be offered a "mental health" contract which is 2-years long with the exact same terms. However during all this time that they are "evaluating" you, you will not be granted your license, will not be allowed to work, and both RAMP and the BON it seems intentionally drag their feet on getting you your license. For example, I was first referred to RAMP in September of 2019, RAMP did not give me a decision about my evaluation until March of 2020, and the BON did not grant me my license until June 2020. And I've heard of people waiting much longer.
I saw another response to your post recommending you get an attorney, but I don't recommend that. Everyone I've met that got an attorney involved or tried to fight RAMP got nowhere and instead ended up starting the program way later, now with the addition of thousands of dollars in lawyer fees to pay. The BON totally endorses RAMP as an alternative to discipline, so there is no other option. There's no legal battle to fight, much less win. I'll link the RAMP guidebook, it outlines all of the rules and restrictions you'll face as a nurse practicing while in RAMP so you can get an idea of what you're potentially facing.
I kinda feel like this was off the rails from your original question but when I was in your place I wished I knew what was coming from someone with the same perspective as me. Everyone else seemed to have major legal issues and substance abuse issues, mostly either showing up to work high or diverting drugs. Based on a DUI 20 years ago I'd say there's a decent chance they'd let you go, however a recent public intoxication charge makes me think you're likely to be told you need monitoring. But as I said, it's hard to predict because people in two identical situations will be treated totally differently. And vice versa, once you're in, regardless of what brought you to RAMP you're all treated exactly the same. Hard and fast rules and strict restrictions on your nursing practice with no exceptions. Basically, if you're working in a different state with no issues, I'd avoid NJ altogether. Once RAMP gets involved they'll notify or require you to notify the BON in any other states in which you are licensed. IMO, it's not worth it.
https://njsna.org/wp-content/uploads/2021/03/final-2021_ramp_participant_guide-revisions-2-25-21.pdf