I've seen people do their own mozzarella and it seemed easy. Any tips on how to get started (equipment, ingredients, recipes)? What about blue cheese and other stronger cheeses?
Making Mozzarella is not fantastically difficult, but certain things during the process are critical, probably the most important is temperature.
If it's your first time making cheese, you might find the buying a 'starter kit' the easiest way to get up and running. These will provide you with all the important items you needm such as rennet. If you feel brave, then you forego the kit and dive right in.
For Mozzarella try to find Buffalo milk, which is what 'proper' Mozzarella is made from. It's lower in cholesterol than cows milk, has more protein and makes a much richer cheese. If you can't get Buffalo milk use the best full fat, non-homogenized milk you can find.
Here's a recipe I've used before MOZZARELLA
Here's a link with the differences between Buffalo milk and cows milk
Whilst it's quite possible to make virtually any variety of cheese at home, some cheeses, such as blue cheese, require a place to develop at the correct temperature and for quite long periods of time. ideally, this would be a temperature around 10c with a humidity around 70% and a time for maturing at around 2 to 3 months.
Here's a good place to start:
Ricotta would be a good first cheese to make. It is a fresh cheese so doesn't need any aging, you can make a batch in all of about 30 minutes with very simple ingredients and the taste difference with store bought is spectacular.
There is a question that has several answers with ricotta cheese recipes (including one I've used) Making (or substitute for) ricotta cheese?
I've actually had success making a soft cheese using kefir fungus to turn the milk instead of rennet; this has the advantage that you don't need to keep buying more.
After you've fed the fungus, keep the produced kefir in the 'fridge for a night. Dilute with fresh milk, no more than 4:1 milk:kefir, and keep the mixture at room temperature for another night. Heat to ~30 degrees, and keep at that temperature, stirring occasionally, until it turns - could take as long as half an hour or so to start, but once it goes it goes pretty quickly. Drain through sterile cheesecloth or muslin to separate the curds, then proceed as usual.
Doing mozzarella at home is quite difficult.
The hard part is doing the curd (coagulation of milk with rennet or an edible acidic substance). This is a common requirement for doing almost any kind of cheese, and although it may seem not so difficult, it is actually very hard to do a satisfactory curd. This is the reason why the most easy cheese to do at home (ricotta) is actually not a cheese!
You can however try to buy from a dairy some curd to "practice" at home.