If you're in North America, get Revolution. If you're in Europe, get Stronghold. For either one, get the lowest concentration dosage (kitten/cat). A vet has to prescribe it, and will calculate a dosage intensity and frequency based on your hedgehog's weight and the severity of the infestation. The medication is alcohol-based topical, which means you don't want to bathe your hedgehog's shoulders the day before, during, or after treatment. It also means you'll need to store the unused medication in a cool, dark, place, or it will evaporate between treatments.
If you live elsewhere in the world, those two medications may not be available. If you list a country, the users from that region may have better advice for you.
You'll want to wash everything (using a bit of vinegar in the rinse is a deodorant and disinfectant) to decontaminate it.
The common experience on the board is that hedgehog mites are them-specific and don't seem to contaminate other pets. They certainly don't go on cats, dogs, or humans. I don't know about other small furry mammals, though -- it may depend on which of the particular mite species your hedgehog has, and it may be easier to just treat the rats as a precautionary measure. As the vet while you're in for your hedgehog.
If you haven't seen it yet, the
West Coast Hedgehogs book is an excellent resource for new owners.
And, to combat the shame, mites do not necessarily imply a poor standard of care. It's easy to get infestations from unbaked wood (some wood shavings, wood cages or accessories...), from playing outdoors, or from other hedgehogs. There's also been cases of no apparent infestation vector, they just ... show up. It happens to every hedgehog sooner or later, but luckily it's a fast fix!
The reason this board is so anti-Invermectin is that it's a lot easier to overdose than Revolution, and has a lot harsher negative side-effects during an overdose. Even worse, hedgehogs can develop negative reactions over the course of treatment (being ok for the first one, but having bad or even fatal reactions to the second). Do not allow an Invermectin injection. If it's the only available treatment option, have the vet apply it topically instead. In contrast Revolution/Stronghold is harder to overdose, is less likely to provoke negative reactions, and those negative reactions tend to be much more mild (hives, itchiness, swelling, but not fatal).
If you're set on using your friend's medication, keep in mind that it'd still be a good idea to go to a vet and get the dosing and frequency set out for your individual hedgehog (it will be different than it was for hers). It'd also be a good chance to do a general wellness-exam to check for any other problems that your new pet is suffering from, and to establish a positive relationship with a local vet BEFORE a serious emergency happens and you're scrambling.
