recommendation for cartridge for the rega P1

I'm not sure if a Shure M97xE would work on a P1, but for your situation that would be my recommendation: When the Shure's damper brush is deployed, it helps the tonearm negotiate warps and skip less.

Maybe you'd be better off selling your P1 and getting a Technics SL12x0 with the KAB fluid damper. It does the same thing as the Shure brush, but much better. With the Technics' removable headshell and easy-to-adjust tracking weight, you could get a second, heavier tracking cartridge for the more difficult records, or just get a better tracking cartridge altogether. I have a Technics with the fluid damper and use an Audio Technica AT150MLX cart. It is a great tracker and I don't have any tracking or skipping problems. But then, I don't know how damaged the vinyl is that you're trying to play.

Now that I think about it, I don't think you should assume you need more tracking weight. I get the feeling you still have the "tape some pennies to the headshell" mentality. Here are some other things to look into:

1. Have you ever cleaned your stylus? It doesn't take too many playings, especially with older, beat-up records, before you stylus gets gummed up with vinyl, fuzz, and dirt, baked onto the stylus. This increases the diameter and changes the shape of the stylus to where it can't sit as deeply in the groove as it did when clean. The best stylus cleaner is a Mr. Clean Magic Eraser. Use it dry, and either lower the stylus onto the Eraser several times, or GENTLY stroke the stylus from front to back only a few times. Then use a soft artist's paintbrush or stylus brush and brush the stylus again to clean off the abrasive residue left behind by the Magic Eraser. Repeat this process after every two records for the next couple of weeks, after which you can take it down to around every five records.

2. Have you ever cleaned your records? The only time my records skip is either because of a pressing defect (very rare) or some gunk in the groove, bumping the stylus out. A concentrated cleaning at the skip spot usually fixes it. I have many records that are 40 to 50 years old, and I track my cartridge at 1.4g. I hardly ever have a problem with skipping records.

3. Check your tracking force. The P1 comes with cartridge factory mounted and adjusted, but I suspect it could drift out of adjustment. Get a stylus gauge and make sure your cartridge tracking weight is somewhere between the factory recommendation of 1.5 to 2.0g. If the stylus is not tracking at that weight you have to move the tonearm counterweight following the instructions in your owner's manual until tracking force measures in that range.