Suddenlink

Assuming there's nothing special about Suddenlink and it uses a CableCARD and possibly a Tuning Adapter then the Roamio, Bolt, or Edge would all work the same for you.
My personal recommendation nowadays is always a used Roamio Plus or Pro because of the standard size case and 3.5" format drives.
What are your needs?

Thanks for your help. My goal is to use the right Tivo box as my main unit and the Tivo mini's for the additional TV's in the house. Years ago, I rented this same Tivo setup through my cable TV provider, Suddenlink. I'm wanting to go back to the same setup but without paying the rent. Ultimately, recording the shows I like and skipping/fast-forwarding through the commercials. It sounds like I'm going to have to get a CableCard from Suddenlink to make this all work. Is it the CableCard that allows me to view the channel line-up in my area?

A used Roamio Plus/Pro with lifetime service and a mini would do it and most likely for under $400 all together.
Yes you would need a single CableCARD and while a PITA to get them properly paired with some operators they are really no big deal.
The Roamio also lets you have the option of if you want the old classic Tivo interface vs the new "it just looks like another cable DVR" interface that has a few more bells and whistles, neither is "better" it's simply which you prefer.

Swapping interfaces isn't simple, but it's also not hard, however its a one way trip from old to new if you want to save your recordings, if you roll back from new to old you will lose any recordings on the unit.

I guess what I'm trying to say is... I would like to sign up for Suddenlink TV service if they will provide a cablecard for a Tivo box I would like to purchase on my own. I don't have a need to store recorded shows or movies. Typically, I would just record something during the day and watch it later that night and then delete it. Most importantly, skip or fast-foward through the commercials. Would the channel guide come from Tivo or Suddenlink?

FYI - I would NOT recommend trying to get a CableCard TiVo working with Suddenlink anymore - my story here.

If you get a DVR from them, it might be a TiVo or it might be their Altice One box - which does not use TiVo software (I don't have any experience with it).

I currently have the a cable card installed in a TiVo Premiere Q that Suddenlink provides me. Can I use my existing cable card, and use in a my own non rented TiVo Premiere XL4, or do I have to get a whole new card?

No, you have to get a new CableCard from Suddenlink. Every CableCard must be paired to the unique ID of each TiVo device, so pulling it out of their box and putting it into yours would result in the card not being paired and it not working.

If you have a working TiVo from them, I'd recommend sticking with it, as a new DVR from them is likely to be the Altice One box (depending on your area). Personally, I would not buy a new CableCable Tivo in 2021, as since there is no FCC requirement to support them, it's like buying a new printer that you can't get replacement ink cartridges for -- it's DOA.