You are (perhaps intentionally) missing a couple options that IMO have excellent potential in a basement. We had cork floors in our last home and are currently shopping for the same for the house we are remodeling right now. The are warm (much warmer than concrete or tile) and soft on the feet. Also engineered wood products can be made for below grade. With both of these you need to have a dry basement. If you have any chance of water/flooding then not good choices. There is also a product of stone/expoxy (everstonefloors.com one seller) that really would be an excellent choice IMO for a basement that might have some water. I went to their store and it really does look very nice and it will not be bothered by moisture as it allows the slab to dry upwards. It's fairly expensive however.

If you don't want to install underfloor heating mats for the porcelain tile (which I would do, but raises the price) then the vinyl will be your best choice. The stained concrete is an expensive choice, usually amounting to 2x the amount of installed tile. With you investing in finishing the basement, you need to be sure that any moisture issues are addressed first by double checking the key mitigation factors such as proper guttering, overhangs, and the slope away from the house. You can still have all of those things and still have a moisture issue, so again, before you spend money to finish things, make sure that you don't have those issues.

As much as I love the look of a beautifully finished concrete, it is cold, hard, loud and it can be SLIPPERY. It etches and stains BEAUTIFULLY. Yep. It etches like marble. It stains WORSE than marble. It is harder to maintain then marble. And above all else, many homeowners cover up their concrete inside of 7 years....because it is so hard to live with. The concrete floors that have the BEST wear and the BEST lifespan and the LEAST amount of problems are epoxy coatings. Not the "over the counter" DIY garage epoxy finishes at Home Depot, but the professional grade epoxy finishes that takes an epoxy specialist to deal with. A basic clear coat epoxy (nothing special that is SUPER slick when wet) can start around $7/sf. That includes the labor and the prep to get the epoxy to stick. If you need additives (like colour or grit) then the price goes up. A stunning 3-stain finish coated with clear epoxy + grit additive to increase the slip resistance = $15 - $25/sf. Finished concrete floors are a lifestyle choice and not a cost saving measure. And even then, they are often covered up because they are cold, hard and loud. The echo created by the concrete is impressive. It takes quite a bit of extra noise insulation in the walls and ceiling to dampen the sound bouncing around because of the concrete. If you wish to try to live with them, I would suggest getting them prepped and add a microtopping that is burnished (ground and polished) to a lovely sheen. Then leave them be for a while. Yes, they will stain. Yes they will etch. And yes they will crack (spider web like cracks are absolutely normal and to be expected/accepted). Once you have lived with them for a while (even if it is just to get through the renovation) you can decide if they are the floors for you. If you decide to cover them up after all, then the only thing you have done is made a PERFECT subfloor that is ready for ANYTHING. If you go ahead and "finish" them (with stain, epoxy, urethane, etc) but decide later on to put down something else (like tile or stone), you will find you need to get rid of the product you put on them (grinding or shot blasting all over again). The "finish" is considered a contaminant that must be removed before a permanent floor can be put down....including vinyl.

I have 3000 sq ft finished upstairs- 3 bedrooms Most people want 4. In order to market the finished space currently in the basement as a bedroom, it has to have a window, which it does not. We are on 61 acres and most people who want this type of space already have a big family, have parents living with them ,or want enough space for extended family to visit. We have had the house for sale as is and that is the feedback we have gotten from some of the lookers. We do not have to move, but are senior citizens, and it is increasingly difficult for my husband to manage the upkeep on 61 acres. Finishing the basement will allow us to advettise 6000 sq ft vs 3000 and more likely get an offer we will accept. However, we are thinking about giving the potential buyers an allowance to finish the floors as they see fit.