When you first bring home kitty you need to have a litter box in place where you are happy with it. This is because it is the very first thing you do when kitty comes in the house on day one or you are asking for trouble already. Set it away someplace but make sure kitty sees it right away and sniffs it.
For cat potty training there are all kinds of litter boxes on the market and you can splurge or go low tech or price it is your call. They have automatic boxes but it may make small kitty feel uncomfy and unwelcome. They have covered boxes but kitty may be too small to get into it on the step up. Covered boxes will retain smell better than uncovered. You can always start with cheap open and move to the automated later. Warning, the automated box may scare kitty from using it again if it goes into work during a bathroom break, so make sure you control the movement. Kitty may abandon the box if scared and move to another part of your house.
When it comes to choosing litter do not spend much time. cares less and there are so many on the market.
You just pick the best choice for you be it fresh smelly, auto clumping or whatever.
However, you may want to stay with the same litter the breeder used or shelter at first to make the cat feel more at ease, then you can switch after a while to whatever you like. Scoopy, clumpy, cedar, crystal they are all good. Some are for multiple cats to reduce odor.
Litter mats are what you put underneath the litter box so when we train the cat we don't have litter scattered everyplace. See the Cat will scratch at the litter and then cover it up and may spray the litter all over your floor. This is just natural instincts of the cat and is no problem. He may also have some stuck in his claws as he tracks it away. Therefore, put a mat or something under the box for you ease of mind and clean house.
David K is a Cat Training expert and has potty trained hundreds of cats and helped cat owners train their Cats across the globe. Cat Training [http://cattrainingonline.com/cat-house-training-101.html]