Your HVAC expert who is designing the system should explain the requirements that the manufacturer has for their particular system. In general, in your situation, you will need lower temperature loops closer together rather than the traditional higher temperature loops further apart. The whole system has to be designed for the water temperature that you will need, as well as the PEX placement distance. Floor coverings also has to be taken into account in the plan. Rubber and carpet actually have insulative power (R values), and are not conductive to easily passing the heat through into the home. That has to be calculated when designing the system, and it will increase the lag time to temperature changes, which is already radiant's biggest drawback.

Currently the floor can receive sheet goods - that's it. Carpet, sheet lino or sheet vinyl. The wonkiness of the concrete prevents everything else. To correct the wonkiness, you need to have the paint removed = abatement. Which is something you don't want to do. Mind you, once the abatement has occurred, you can go ahead and have the concrete flattened/dealt with and then you can have ANY FLOOR you want. Whenever you want. For as long as you want. Until then, you can work with "sheet" materials like carpet, lino or vinyl.

When we bought our 1928 home, we assumed/ hoped there would be hardwoods under the upstairs carpet we ripped out, but we were wrong. We decided to do new carpet that was affordable & looked alright, mostly because we had small kids & were in a rush to get the house livable. But we also weren’t concerned with safety as much as the potential that our arts & crafts-loving kids would destroy newly-laid floors with their spills, paints, markers, hot glue guns, etc. Fast forward ~10 years and our kids did very much wreck their carpets, but these are nearing the end of their useful life anyways, and we’ll feel much better replacing them with new hardwoods as our kids begin their adolescent/ teenage years. So if it were me, I would save some $$ by carpeting your entire upstairs now, but build wood stairs and put a runner on them. Reason for wood stairs: besides cohesiveness with your main level’s hardwoods, I would assume it’s harder & more expensive to retrofit your stairs to wood after they were originally built for carpet. And building codes for stairs nowadays make them pretty safe, and a runner will protect the wood from your kids. And if you go to sell or you are still there when your kids are older, you can always convert to hardwood at that time (vs having to refinish your floors and replace untold numbers of rugs during the kids’ more destructive years). Good luck!

I have always liked the slate or slate look flooring with wood paneling. Maria Killam has a post where she shows some great matches of LVT to wood floors - we've come a long way in the look of LVP, so I wouldn't just say it all looks fake next to the real thing. I don't think I would want wood look LVP with your wood paneling, but it could be done if that is what you like. I agree with palimpsest that you could find some nice tile or stone look LVT. I think this might be nice with your walls or possibly this: