In regard to which ingredients to avoid, quite frankly any of them can cause adverse reactions. This includes cyphenothrin, imidacloprid, permethrin, spinosad, milbemycin oxime, pyriproxyfen, ivermectin, moxidectin and imidacloprid.
If your Beagle is doing just fine with a certain product and is not having any adverse reactions, we recommend not making any changes.
If, however, you are wary of brand or suspect that it is causing some adverse reactions, it may be best to try a chemical-free product (when you can, for fleas and ticks) and think about changing base ingredients for heartworm protection.
We recommend Advantage Multi (this should be available at your local pet supply store), because while there is no guarantee, what seems to be most well-tolerated is moxidectin and imidacloprid, which are the ingredients in this.
This offers protection from heartworms (both adult and microfilaria, which are the offspring that live in blood vessels), fleas (both adults and eggs), roundworms, hookworms, whipworms, and sarcoptic mange.
Across the board, Advantage Multi offers what Trifexis, Sentinel, Heartguard, and others cannot do, in regard to a wide range of parasite stages and phases. This includes killing flea eggs and heartworm microfilaria.
While this is not marketed as tick repellent, it may work in low-risk areas. It cannot be not labeled as so; this would mean having to meet higher guidelines meant for high-population areas.
So, if ticks are not a high concern for your Beagle in the area where you live, using this along with a chemical-free tick repellent will usually cover all the bases.