clean eating can be done gradually, but the end goal should be to eliminate all bad foods (imo). but having said that, the best diet is the one you can stick to longterm.
the science is still out on grains but my inclination is to say that wheat, rye, barley type grains should be avoided. corn and rice seem to be relatively harmless.
more seafood is good, in spite of the mercury issues. most people don't seem to eat nearly enough seafood and upping their intake a little would benefit them much more than the risk of harm from mercury. so once a week is a good goal if you're not there :)
the thing with meat is that if you want to eat clean while being a carnivore you need to be very careful what meat you eat. processed stuff is generally harmful, but there are some exceptions. with beef you always want to go organic grass-fed if you can to avoid most of the hormones and antibiotics. if you can't afford this go for super lean cuts, as the antibiotics and hormones are absorbed in fatty tissue and you'll get higher levels of it eating high fat meats.
lamb, buffalo, pork (kinda...), and stuff like ostrich and yak are better alternatives because the laws at least in usa are more strict about when you can give antibiotics, and the use of hormones is generally not allowed.
if you can't give up your bacon find uncured, hopefully without added sugar. and the world health organization found that the more cooked a piece of meat is the more carcinogenic it is. so go with rare or medium-rare.
eggs are almost a must if you're not vegan. so much nutrition packed into such a tiny package :)
veggies always, every meal, as a snack, whatever. same with fruit but limit if you're cutting. never eat dried fruit, it's so bad for your teeth and is basically candy. tons of sugar, leaves you hungry.
kebabs can be plenty healthy. make your own if you have the time. add veggies.
the biggest bit of advice i can give on diet is to stay far away from processed