I really enjoy mutations and so have changed the rules a bit. Things mentioned here are in addition to what races currently get unless noted. Please note these are rules, I use in my game, your game may be different.

Mutation Point Distribution

Mutant Humans get 10 total mutation points and must roll on the charts to distribute them between Physical and Mental and Ordinary, Good, and Amazing. They still have the 4 Drawback points. They also may have one Perk and one Flaw from the Alternity Players Handbook.

Pre Existing Races (Dabbers, Sleeth, and Weren) get to roll on the following chart to see if they get more mutations

They may not select any Perks or Flaws.

Mutant Animals get the standard 7/4 and are allowed 1 Perk and Flaw. They also get reasonable free mutations based on original stock.

Androids do not exist because the invaders don't either. No aliens in my Gamma World. However if they did, they would get no mutations. 

PSH may take up to 4 Perks and Flaws for 1 point less than listed.

In my game there is no such thing as the DNA lockout, but items designated for Androids and Humans (a) give a +1 penalty to non-humans when they use them. Items designated Human only (h) give a +2 penalty.

These penalties will always apply, no matter how skilled the non-human PC is.

Mutation Strength

After some hardcore 4th edition gaming, finding out that 5th doesn't give mutants a bonus (or penalty) for their mutation based on a mutation score I was a little distraught. The more I look over it the more I'm thinking something along the lines of: 

Use this rule for activated mutations that don't already clarify their activation result. These mutations get a Mutation score based on their attribute. Prior to using the mutation roll a Feat check against the mutation score. Modify the opponent's resistance check by Crit. Fail = -1 F = 0, O = +1, G = +2, A = +3. That'd cover a lot of the mutations with one basic house rule...got to go through and see which ones it doesn't. The higher the mutation score the better the chance for a good or amazing check, giving the opponent a larger disadvantage.

On a case by case basis I also make the mutations that cause damage or have variable effects rise in potency by adding a little bit to the total (d6s to d6s+2 for example) if the players spend XP on them (I know the correct wording is Achievement Points, but I don't care.) To raise a mutation score a player just follows the guidelines for raising an attribute.

Character Generation
Derek Holland

Base 60

+5 to physical abilities for most animals*
+10 to mental abilities for humans and mutant humans
+10 to physical abilities for hard-bodied arthropods and other animals known for "toughness"

*Animals start with 60 and they can add to their stats as desired. In an attempt to simulate the 4th edition physical ability score variations for animals each physical attribute gets a set bonus. Here are 12 common mammals found the Northeastern US: