Yeah I barely eat any meat these days. Not on purpose, it just doesn't end up happening.
It might be a good idea then if you did some reading about how to make sure you get enough of the "good stuff" from a vegetarian diet, even if you have not decided that you are a vegetarian.
Fingernails need adequate protein in your diet. If you are not eating meat, you need to make sure you're getting enough from beans, tofu, mushrooms etc. Dairy protein is another option obviously if you can digest it, and eggs too if you're OK with them. Getting adequate iron is another issue with nails and hair, because iron from vegetable sources is more difficult for your body to absorb, but keeping up your Vitamin C intake helps with that. Some trace elements including zinc, copper and sulphur are supposed to be good for hair and nails. Shortage of biotin (AKA Vitamin H, Vitamin B7) may cause problems, but it is rare. Biotin is claimed as a "magic ingredient" in some skin and hair care products, but I think it's a bit bogus.
I am very skeptical about "strengthening polishes" quite frankly. I'd look to protein intake, and consider taking a multi-vitamin with minerals, though I know that good ones are not exactly cheap.