No matter how careful you are to treat your outside plants for insect pests in the fall, before you bring them in for the winter, you'll likely encounter some anyway, before winter's over.
The last couple of years, I finally got the fungus gnats under control. I learned not to overwater and that was a huge help. I'll see one now and then, but not nearly like I did that first winter that I had so many plants in the house.
That first winter, I also had problems with white flies on the Brugmansia plants. I thought I'd never get rid of those. Took me half the winter to do so. Back then, I didn't pay much attention to using organic means to rid my plants of them and while I can't remember exactly what I used, I know it's not something I would use now.
One pest I've had to battle every single year since are spider mites on my Brugmansias. The little boogers seem to love them. They don't show up right away and I always wonder where they come from, since I have never had a problem with them when the plants were outside. But just let me bring them in the house and eventually there they are, clustered on the stems and leaves, in their webs.
The best thing I've found to control them that I'm comfortable using in the house (or out, for that matter) is Neem Oil. It doesn't smell bad, isn't toxic, and it works. It may take more than one treatment to rid the plants of them, depending on how badly they're affected, but once they're gone, they're gone for good.
For this reason, I've chosen to carry Neem Oil concentrate in my OpenSky shop. I only carry products there that I believe in. Most of them I use personally.
Neem oil comes from the fruit and seed of the Neem tree (Azadirachta indica), which is native to India and is widely used in organic agriculture. It's easy to mix the concentrate with water and more cost effective to buy that way, even though it's not an expensive product anyway.
I've found it to be a great multi-purpose product you can use as a spray to control spider mites, aphids, white flies, thrips, mealy bugs, and fungus, among others.