Rennet (whether liquid or tablet make sure it's in date and has been stored at the right temperature) and optionally a starter culture, plus if you're using pasteurised, homogenised milk you'll need calcium chloride to get a decent firm curd.
For equipment, at a minimum: a decent digital thermometer, cheese mats (expensive but last forever), hoops if you want to make cheeses like Camembert. A double-boiler or bains marie can be useful so you have good temperature control. Cheese cloth. A press if you want to make harder cheeses.
Based on my experience I'd suggest starting with soft cheeses - fresh cheeses you can eat right away like Paneer or Queso Fresco, or bloomy rind cheeses like Camembert, which you can eat within a few weeks, or cream cheese which you can flavour with all sorts of things. That way you learn the basic steps (which are the same for many cheeses up to curd set) and have immediate results you can taste and enjoy.
I like cheesemaking.com a lot, sign-up for their emails and you'll get 2 volumes of their recipe book emailed as a PDF. I used their Camembert recipe and the results were really good:
http://www.cheesemaking.com/Camembert.htmlThe downside of pressed cheeses is the amount of extra equipment you need for consistent results. And for cheddar the length of time you have to wait before knowing if it's a success (months), assuming everything goes well up to the point of ageing. You also need the right environment to age it in.
Re starter cultures - although the recipes will tell you to use this or that starter, I've used Flora Danica for all my cheeses to date, adding penicillium candidum for the Camembert to develop the right rind mould. As long as it's the right type of culture (mesophilic vs thermophilic) you'll be fine - maybe not the *exact* same as you're used to, but that's half the fun of doing it yourself.
They are expensive, but you can make them up and freeze them - I use ice cube trays, then turn them out into tubs. Should be good for up to 12 months.
HTH, I've loved making cheese this year and plan to continue with shop-bought milk now we've stopped milking.