I try to outline a few basic points.
Meals should be either meat, or dairy. That means no meat is allowed anywhere close to dairy, not in cooking, not in serving, and viceversa. Meat also includes poultry. Meat (and poultry) needs to be kosher certified because it must be slaughtered and prepared in a specific way and by an observant jew.
For dairy, the cheese has to be kosher certified, but with milk or butter, you can rely upon the regular ones.
As I mentioned, you can eat fish in a meal with meat, but there are restrictions. You can't cook them together and you can't eat them together. If you wish to do that, you have to cook separately, then you eat the meat dish, then you eat something else (vegetables, eggs, bread) and then you eat the fish. You can also do the reverse order. There is no restriction with fish and dairy.
You don't have to buy certified fish, but you need to be able to recognize kosher fish, because not every fish is. Or you can make a list of fish you ordinarily buy and have someone read it.
Eggs can be eaten with milk or with meat. Same with vegetables. When you buy them canned, the easiest thing is to search for kosher certified, which in fact are no more expensive than competitors. If you buy them raw and clean them, you have to check for insects and parasites. There are guidelines that you can find on the websites of reputable kosher certification agencies. You can also find on the internet plenty of discussions about the kosher status of coffee-based beverages. To tell you the truth, I only drink black coffee.
There is one more item which would require kosher certification, that is wine, grape juice, wine vinegar. The beers and liquors, as long as they are made from kosher ingredients (e.g. there is some tequila which includes a nonkosher, and disgusting, ingredient) do not require certification. Soft drinks, you can usually find them certified. Mineral water and sparkling mineral water does not require certification, but there are brands who have certification anyway.
There are restrictive rules on Pesach but that's many months away :)
The other thing you should know, is that your kitchen cookware, dishes, etc. will eventually need to be rearranged, because it can absorbe nonkosher taste or it can create a forbidden mixture of milk and meat. Perhaps you should ask someone to do that in person, because it is difficult to explain over the internet.
Also, of course, nonkosher food (e.g. for the cats) has to be prepared separately and care should be taken when you use and store the food, the pots, etc.
I wish you much success!