Cacti

I often post cacti bare-rooted, so that when they arrive at your place, you need to pot them up again.

Use a good ratio of potting mix to drainage aerators (pumice or perlite).   Generally cacti need a ration of 50:50.  Some, like lithops, need even more pumice.    Others are fine with lower ratios.    Look at the potting mix you use as your base first.   Some already have a fair amount of pumice, and other types of potting mixes have mostly organic matter.   

Don't choose too big a pot.    Partially fill with mix, place your plant in, then add more mix around it.
If you have a really spikey cacti, use tongs, paper or something else to hold it so you don't get any spines in your hands.   Gently firm the soil around the roots.   I often use a small stick or my latelling pencil, keeping fingers out of trouble.

Now, do NOT water your plant.    Place it in its new environment and leave it until it is dry.    If its winter, I wouldn't water at all.    If it is summer,  water about in a week's time.   This delay ensures that any damaged roots can heal without extra water affecting them and causing rot.

Cacti are not suited to being house plants, although often people do grow them inside.    Ideally, most of them are fine being outside, maybe on a deck so that you can control how often they get watered.    Give them the sunniest and driest spot you can find.