First, you need a long straight edge. Cutting a three inch wide strip off the 8' edge of a sheet of plywood is an inexpensive way to get a long straight edge. I long level or a clamp on saw guide also works.

Plumb is a vertical measurement. Plumb is actually 90 degrees to the ground/floor. Plumbing the back splash is not as critical as having the wall level.

So, get the straight edge and place it across as many studs as it covers(using the factory edge of the piece of plywood). It should cxover at least 5 studs and maybe 6.

Find the high points. The low points are not as important unless they are over a half inch low---not usually a problem. Use a marker or paint to mark any high points more than 1/8" high. In have a power planer to remove those high points(after removing ALL nails/screws!!!). You can buy a Ryobi power planer for about $35 or so.(Mine was $120 about 10 years ago).

Or a hand plane---but a good block plane will be at least $35 and need sharpening and adjusting---which takes experience and practice.

If the hich points are onlt 1'8" or so high, just use a sander---a random orbit model removes wood faster than the square finish type. Ryobi makes those also. HD/Lowes/etc. sell them.

Crooked is not an issue---flat and level will do just fine.

I use regular sheetrock for backsplashes. Never have had a problem when the finish surface is correctly installed and sealed.

When the sheetrock is installed, you do need to tape and mud the joints/seams. And that can cause bumps if too much mud is left. You won't get the sheetrock perfectly flat, but as close as possible is fine.

Once the sheetrock is installed, follow the instructions for the material you will use for the backsplash, you may need to seal/prime the sheetrock before installing the material.

One good idea is to buy a DIY book( at HD/Loews/etc) on how to do backsplash installation. They are usually quite informative and for the $10 or so, could save a ton of mistakes.

Thank you handymac for your detailed instructions! I really appreciate it. I am dealing with about 13" of exposed studs between the upper and lower cabinets. I forgot to mention earlier that we also have new countertops already installed. (Now I'm wondering if they knew what they were talking about when they said to remove the old drywall/backsplash and go to studs BEFORE the countertop is installed...might have made things easier for them to install the countertop but I wonder if its made it harder for us now.) Anyhow, I've never used a power planer before. I sure would hate to scratch my new countertop :(

You could use shims to bring any low sections out even with the high ones. That usually is a long involved process.

Using a power planer for this job would actually be using it incorrectly. They are designed to be used along the length of a piece of wood. To knock down the high places, you simply run it perpendicularly to the stud. It is not pretty, bnut it is covered up anyway. And shims look odd too.

In a space of 13", I doubt seriously if you will have a problem at all. Get a straight edge and check before doing much of anything else.