Although it’s very much a cultural issue, I prefer having separate shoes for when I’m at home. You can change between shoes at the porch, and doing so will ensure that you don’t track in filth. Indoor shoes can also provide your feet with support and, at the same time, be more comfortable than lace ups.
There are a variety of options. On the more “formal” side, there are Prince Albert slippers, which are typically velvet and have quilted silk linings. The English aristocracy used to wear these when they received people into their homes. They were worn with tuxedos and smoking jackets, but in the past few decades, they’ve migrated to the more casual side of the spectrum. I think they look quite smart with a pair of casual trousers, button up shirt, and a sweater. Black is the most traditional color, but brown, navy, and British racing green work nicely as well. I like them plain, but if you get an emblem, I suggest that it be of something with personal relevance (e.g. your initials, a sport you play, or a school you attended). You can buy such slippers from Brooks Brothers, Stubbs & Wooton, Broadland, Bowhill & Elliot, and Shipton & Heneage. You’ll also find that most major English shoemakers have them for sale.
For more casual options, there are Grecian, mule, and moccasin-styled slippers. These typically come in leather and sometimes have sheepskin lining. I think such slippers look best with a heel cup, but the mule style will be easier to take on and off. Drapers of Glastonbury makes really excellent models, and Pediwear has them for pretty attractive prices. You can also get some handsome ones at Brooks Brothers, Morlands, Jeremy Law, and Mr. Porter.
Some American men may want even more casual options still. For those men, I’d recommend LL Bean, Lands End, and Ralph Lauren. I personally don’t find those styles to be as attractive, but they can look more suitable if you wear jeans or sweatpants at home. You can also check out Muji (both the European and American webshops). They have slippers at extremely affordable prices.
Finally, two additional pairs I think you should consider are the travel and bath slipper. If you travel a lot, a pair of travel slippers can be nice for when you’re at the hotel. They’re also wonderful for long flights since your feet swell during air travel. La Portegna makes some really handsome ones, but as I’ve written before, their shipping is a bit high. I’ve been told, however, that they’re working on expanding their US distribution. The other pair of slippers you may need are terry cotton bath slippers. These should be worn underneath a bathrobe when you’re heading off to the shower. Having a separate pair helps ensure that you don’t stick damp feet into your lounge slippers, which can be bad for both your feet and your shoes. If you buy nice slippers, you might as well make sure they last.
(pictured above: Derek Rose Gower slippers)