Can't add too much more other than to keep an eye on the smoking point. Bear in mind that the more you reuse an oil, the more you lower its smoking point. Start with an oil with a high smoking point, like Canola or Peanut. A lot of folks like peanut oil because of its neutral flavor.
And, peanut oil shouldn't be a problem with anyone who has a nut allergy. It's so refined, that the allergens are no longer in the oil. My oldest daughter is allergic to peanuts, but has no problem with food fried in peanut oil.
As far as frying foods (any foods) being unhealthy goes, it's not. It's improperly frying foods -- oil too cold, frying too long -- that makes it absorb fat. I think Trekker4747 said upstream that if you fry until there are no more bubbles, you've fried too long. That's the key. The bubbles mean steam is still escaping from the food, so no oil is getting in. When the bubbles slow or stop, it means the food can now take on on oil and become greasy.
I saw Alton Brown debunk the "frying is bad for you" myth when he poured the oil back into a container after frying some chicken (I think it was chicken), and all but the very smallest amount of oil was returned to the container.
