We started Teach Your Child to Read in 100 easy lessons and Right Start Math A around this time. Our daughter already knew all of her letters and sounds and we decided to just try 100 easy lessons with her. There is a good chunk of 100 easy lessons dedicated to teaching letter sounds though, so the early lessons were really easy for her and she learned and enjoyed the format. We only did lessons if she wanted to, but she generally wanted to. We would usually average about 3 days per week where we would do school time (sometimes more and sometimes less or not at all). School time is usually around an hour long for reading + math and sometimes we also talk about science/history suggested in the Pre-k core knowledge what your child should know book (what do plants need/ types of animals / George Washington / pilgrims and native americans).
She finished 100 easy lessons in 8 or 9 months and now she's addicted to Bob Books. She's so proud of herself and so excited that she can read that she'll want to continue on well past the 1 or 2 books we actually plan on reading for lessons. She's at 3.5 now and we are working on handwriting without tears to get her writing well enough to do explode the code.
She of course does all of the normal toddler stuff. She loves singing songs, going to parks, playing with her friends, painting (she's been really into water colors lately), puzzles, blocks, toys, playing/watching on her tablet (kids kindle fire), making necklaces with beads, legos, etc.
As for materials, we have a school room that has a bookshelf with the books around her level, a small round kids table with kid chairs that she can sit at to read/write, a dry erase board on the wall (She was really into having us print the stories from the end of the end of each lesson in 100 easy lessons on the board and reading it from there instead of from the book). She also has some miscellaneous toys in her school room separate from her normal toys (a block/bead set with some shoestrings that we originally used for talking about patterns and for helping her develop motor skills as well as some kids board games/memory tile games).
We're fortunate in that she really loves her school time. She loves learning to write new letters (she does the copywork in HWT and then we make her a page with a sentence or two of copy work focusing on the letter(s) she recently learned). She loves reading. She loves her work in Right Start, especially when she gets to use the abacus. If she didn't actively want to do this stuff, we wouldn't be doing it and would have just gotten to it later. Our son is 15 months and doesn't show any interest in sitting still long enough to be read to (other than bedtime) like his sister was at that age. I don't know if he'll be interested to start learning to read or do other school type stuff at 2.5 or not. If not, no big deal. 2 year olds still learn an awful lot just by living and all that other stuff can come later.