In a previous kitchen remodel, we had the same issue in the transition from solid brick to framed. Our choice was a 3x6 border topped with 6x6 field tile on the diagonal. The run was approximately 16' long and the imperfections were not noticeable.

The larger the tile, the less 'wiggle room.' Small mosaics would be most forgiving--that's why they're used for shower pans.

What is the style of your kitchen? Would beadboard be appropriate? I used the inexpensive sheets in my vintage-style kitchen. I know it's not for everyone, but I'd prefer it to vinyl tiles/sheets.

I googled 'vinyl tile backsplash':

Here is a link that might be useful: One option

No matter what you do you'll need to level the wall out. I'd start with a real thin fiber cement board and install it with enough thinset built up in the shallower areas so you have a nice level surface to begin with. Then it doesn't matter what tile you use. Otherwise you'll need to make sure you are careful and put enough thinset on the individual tiles to make it all level.

Please don't use vinyl tile as a backsplash if for no other reason than it seems "tacky". If you are going to have the expense of granite or quartz don't cheap out on the backsplash. If you want a wood look there are many gorgeous porcelain tiles with that look. Any subway tile or smaller that has an uneven, handmade look should hide the look of wall imperfections but it is best to just fix the problem before tiling.

You really need to straighten the wall out as much as possible. It will save you in the long run from future issues.

We have wavy plaster walls, and the advice I got was to choose smaller tiles rather than larger ones. We used 4x4 squares set in a running bond pattern (staggered instead of lined up on top of each other), and that worked pretty well. If I'd had the sense to hire a decent tile setter, the wall would have been leveled before the tile went up, and that would have made the biggest difference. But even with our semi-incompetent tile setter who left the wall wavy, it's not too bad. The offset pattern definitely helps. Two other things that would have helped in our case would have been to use imperfect handmade (or handmade-look) tile and matching grout. Our tile is perfect machine-cut squares with slightly contrasting grout, and those things show the waviness more; but I can honestly say that after a few months I don't think about it -- not like I did at first when I wanted to run the tile setter out on a rail. lol.

So: hire a good tiler (or learn to do it yourself if you are the careful detail-oriented sort), use 4x4 or 3x6 tile, choose a tile pattern that will mask imperfections, and level the wall with thinset or whatever first. If the wall is leveled then I don't think it'll much matter whether you use handmade-looking tile or machine-cut, or what color grout you choose. For our kitchen I liked the straight machine-cut tile better than the faux handmade tile I saw, and I definitely wanted contrasting grout; those are just personal opinion design decisions that'll depend on your taste and the style of your kitchen.

You might want to try something like Jeffrey Court's Fire & Ice. Because it's not uniform thickness throughout, I think you could hide lots of flaws. At least it did in our kitchen.

Jodi-