There are (at least) two different types of stains for concrete. One is a surface coating, the other is acid etching.
The former can work, but isn't as durable/lasting. I believe most of the products you get at the big-box stores are more of a top-coat type of stain.
Acid etching is just that, it's a stain containing an acid that actually etches the concrete. This is the typical type of stain you see in home magazines and such. The etching provides a deeper stain that is more durable and not prone to flaking.
I've done the latter, and applying it is super-easy. It's the prep work that can be a chore--namely if you have adhesive on the concrete already. In our case, we has tile mastic, which we had to dissolve using soybean based stripper. It worked great but was incredibly messy.
If you don't have glue to deal with, however, you should be good to go. Order up the stain (lots of places online to get it). You then dilute it per instructions and spray it on the concrete. I used a garden sprayer for this. You then let it sit for a period of time, and then you apply a neutralizer to stop the reaction.
After that, you apply water and mop/squeegee/wet-vac it up.
Then, you apply a sealer of some sorts. Common options are wax-based, polyurethane, and epoxy. I went with poly as it was relatively easy to apply (roll it on). That said, I don't think it was ever truly waterproof. For your needs, you may want to go the epoxy route.
I would guess that gut (rip/demo to the studs) and re-rock is likely be the best option here - not only best end result at the paint job, but fastest (if drastic-seeming) route to that paint job. Scraping and stripping are awfully slow compered to rocking and mudding.
Best Answer
You don't sand painted drywall. Hit up your paint store and ask them what stain-blocking primer they recommend. Apply that per the instructions, blending it out to prevent hard edges, then paint. If the paint on the wall is more than a few months old you may need to paint the entire wall to get good color uniformity.
You might use a soft cloth and a bit of paint thinner to try and gently scrub some of the stain away so it's less likely to bleed through the primer.