Kinda looks like vinyl sheet flooring. Either way you must take up the flooring and scrape it very good. If its tile I would rent an air hammer with a flat chisel. After the floor is clean check for dips and bumps ( level is not so important) and level it out with floor leveler. Floating floor is a simpler option but I won't touch the stuff and you will get a more possessional job with engineered glue down. Better resale also.

It depends on what type of wood you have and how old it is. In our last house we had 75 year-old birch, and the new planks we added during a kitchen reno always looked a little different (although not enough to really matter...the planks had differentiations even amongst the original wood.) Of course we did refinish the entire floor at the same time... Oak might be easier! In our current house, there are 60 year old red oak floors. They'd been recently refinished (~3 years ago.) We needed to patch in a large section during our kitchen reno, as we removed walls and relocated the kitchen. We simply bought new unfinished red oak (at Home Depot) and a satin poly my DH hoped would match the existing. He expected to have to try a few different finishes and/or stain, but it actually looks identical just as-is. I can tell you----- staining is not the best answer for the long term!! In another part of this house, a previous renovator used WHITE oak, and then stained it to look more like the red oak everywhere else. When we tried to do a screen-and-recoat recently, when adding some new flooring to an adjacent room, we found we were sanding off the stain. So we had to proceed VERY carefully so as not to remove the stain.... otherwise it would have meant a major sanding of ALL the stain, and then re-staining. It was a bummer because there were some scratches and fading that I'd really wanted to fix, but doing so just would have been too big a project. If you want to be able to do easy screen-and-recoats, selectively sanding more where you need to for repairs, DON'T use stain.

The 'Return On Investment' (ROI) is a local one and a personal one. A basic 3" wide red oak strip hardwood has a relatively low installation cost. It is the closest in cost to 'new carpets' being installed. The regular red oak in a narrow plank (with labour and materials) will cost around $10/sf. A HIGH END carpet is going to be in the same range $7-$9/sf (with high end pad and labour). You will 'maintain' the value of your home with the new carpet (no increase in price; no speedy turnover). The ROI is very little. The one thing it prevents is loss of value (or a home with 'flooring allotment' built into the price). The hardwood will offer 25% - 40% ROI. That means the house can be slightly higher (in the mid-upper range for size and location) and can be expected to have a shorter time on the market. There is NOTHING like the advertising that states, "Solid hardwoods throughout". That's a buzz phrase that every Realtor LOVES to use...'cause it moves inventory!

How old are your existing floors? Are they close to the age of 20 years? Are they ready for a full sand/refinish? If they are, simply add more of the same (dirt cheap....honestly the narrow strip hardwood is one of the easiest woods to find and to finance!!!). It is amazingly easy to get the carpet upgraded with 'more of the same'. By adding more of the same, you get to save money....while taking care of the old. The time to add more wood is when the old finish is ready for the full Monty (age 15-25 years....depending on how well the finish is performing). If you don't need the sand/refinish then go ahead and get the same species, the same cut and the same grade as what you have. You can choose the width of the plank. What I would then do is: lay it in a pattern such as herring bone or chevron. If that's too expensive then go with a diagonal install (not my favourite but many people like it). The MOST IMPORTANT thing you can do is: MATCH the wood species and the cut (quarter/rift/etc) and the GRADE (Select, Grade #1, #2, Character, etc). By doing this, you will always have a GREAT match when all the floors are sanded/refinished at that same time. You will never have to worry about getting the 'stain' or the 'colour' to match. You will have already dealt with that because the wood is the same....only the WIDTH is different.