BODY SAFE MATERIALS
Medical grade silicone - Medical grade silicone is one of the most common sex toy materials. Technically silicone is not 100% non-porous, which is why I recommend that folks don't use silicone toys anally and then vaginally without condoms. However, medical grade silicone can be boiled or put in the dishwasher to full sterilize. Although generally soap & water is perfectly fine for cleaning. While it is uncommon, silicone allergies do exist. So, if someone has a reaction to a silicone toy it COULD be that. However, in my experience it's more often a soap residue or irritating lube that's causing a reaction if the toy is truly medical grade silicone. 
Stainless steel - completely non-porous, very body-safe, easy to clean with soap/water or boiling.
Glass - there are two kinds of glass toys: borosilicate and soda lime. borosilicate (pyrex) can go from cold to hot without breaking, whereas soda lime glass needs to be warmed up very slowly or it will crack/break. Glass is a completely non-porous, body safe material. It cannot break inside a person, although i have heard of glass butt plugs breaking if someone falls on their butt wearing it (ie. dancers who wear plugs will they work).
ABS plastic - phthalate free ABS hard plastics are body safe. they are non-porous! These are great options for people who have a silicone allergy. 
Wood - wooden toys, when sealed with a special coating are also body safe and non-porous. No, you can't get splinters from them.
Crystal/Stone - Now, this is sort of a sex toy material debate! Certain brands make crystal dildos from rose quartz and obsidian (among other materials), which are hard and almost completely porous materials. However, jade eggs and other precious stone materials, usually need to be coated with some kind of sealant to be body safe. Otherwise, bacteria can grow in the material and cause infections. However, there are also certain stone dildos and ceramic that are totally safe!


NOT BODY SAFE (with some nuance)
Toys with Phthalates: phthalates are a family of chemicals used to soften hard plastics. They have a tendency to off-gas and can cause short term and long term health issues. Signs of a toy with phthalates: pungent, chemical smell, oily/greasy feel, “sweaty” looking, gooey/melting.
Elastomer - this material is kind of on the cusp. It is a porous material, but the material itself is not harmful or unsafe. If you clean it regularly, or use a condom with it, it's totally fine. Good to note though if using it between partners who are not fluid bonded.
Rubber - often contains phthalates. if it's not pure medical grade silicone, there's no way to know it's definitely not toxic.
Jelly - again, usually has phthalates and other harmful additives. Jelly toys are often really soft and squishy, have a pungent, chemical smell, and will "melt" over time. If folks are really attached to a jelly toy, they can put a condom on it, but I personally wouldn't risk it.
Latex - latex condoms are safe as long as no one has a latex allergy. However, latex does degrade over time (that's why you gotta check the expiration date on condoms!!) Thus, latex sex toys degrate over time, so that's a no for body-safety.
PVC plastic- often contains phthalates, but a phthalate free PVC material has been created. This is the case for the head of the doxy wand which is phthalate free but made of PVC.

 

BONUS: LUBES
Glycerin - lots of lower quality lube contains glycerin. Glycerin is a sugar, so when it comes in contact with the vaginal ecosystem, it can cause yeast infections.
Parabens - Parabens have been inconclusively linked to breast cancer. They are also common in cheaper lubes. No one needs that.
Silicone - Silicone lube is the only truly hypoallergenic lubricant. The silicone molecule is very large, so it sits on top of tissue rather than absorbing into the skin/tissue. For this reason, silicone lube is often the best option for folks who are extremely sensitive or prone to yeast, BV, and/or UTI infections. However, as I said earlier, silicone allergies do exist. Also, some silicone lube does contain additives that can be irritating (like vitamin E or aloe).
Oil based lubes - Plant based oils = GOOD, Kitchen oils = BAD. That means, pure virgin coconut oil and almond oil are great. Baby oil, crisco, olive oil (usually mixed with stuff), and other kitchen oils can clog pores and start infections. (side note: don't mix oils with any porous sex toys (likes ones made of elastomer), because it can grow bacteria and mold in the toy, ew).