Below are some links to equipment with some pros and cons. Let Instructor Ferrito know what you would like to order.
Sparring helmets are of two basics "grades" and for our purposes I don't think that students need anything more than the lighter and least expensive of the two.
For in class sparring I recommend one of these or the other.
Lighter foam sparring gloves will be everything you need for a lower cost.
These are heavy enough for use on a heavy bag or Thai pads and will work well with focus mitts. They may land a little heavy during sparring compared to the light foam options (not linked to here) but not enough to make it worthwhile to buy two pairs of gloves for different purposes.
Here are two suitable shin guard options. One is much more convenient than the other, though it is more spendy. Both are "instep" style so there is something holding them to your feet. However, the velcro option of the pricy option is way easier to deal with after a few sweaty rounds of sparring than the ones that have to be pulled off by your partner. I've seen some students miss half of their sparring sessions dealing with difficult pull-on shinguards. The velcro option will also provide a little better area of coverage. The one big benefit to the pull-on style is that once it's in place, it's not going anywhere, whereas the velcro style can slide around just a touch, though I've never had any real problems with them.
Mouthpieces are a personal preference, and I will simply order a few very basic mouthpieces for everyone to try. If they're working well, no sense in spending your money on anything different.