Oscar Wilde said correctly that trousers should hang from the shoulder, not from the waist. Belts have no place in the tailored wardrobe, and should basically be relegated to wear only with jeans or chinos. Belts function poorly because they require adjustment several times per day; because they tend to constrict the waist; and because they cut the body in half visually, which is especially bad with a suit as they destroy what should be an uninterrupted line between jacket and trousers, as well as creating a bulge underneath a jacket or vest.
By contrast, suspenders (sometimes called braces) maintain the suit's line and are more comfortable to wear: they require no readjustment during the day, don't constrict the waist, and promote air circulation through the trousers.
Clip-on and elastic suspenders should both be avoided, both because they lack style and because they function poorly: elastic suspenders don't really "suspend" the trousers; clip-on suspenders damage the trouser fabric into which they bite for their grip, and tend to come loose during wear, especially as they age and the clips lose their tension.
Instead, suspenders should be attached by leather tabs to buttons sewn on the waistband of your trousers. The buttons can be sewn to either the inside or the outside of your pants; while the outside is more traditional and probably slightly more comfortable, I find it to look a little "sloppy;" I prefer the buttons on the inside, which makes a crisp, horizontal line between suspender tab and trouser waist.
There are several firms that make quality suspenders, but far and away the best are England's Albert Thurston, which are superior for two reasons:
1. They're sized, which puts the metal adjusters near the bottom, where they belong, instead of near the shoulders.
2. The leather tabs are available in white.
Suspenders with white tabs, as designer Alan Flusser has noted, are one of the sartorial bona fides that identify you as a sophisticated dresser.
Perhaps more importantly, they reduce the number of required suspenders in your wardrobe by 50%, because white tabs can be worn with any color shoe, while black or brown tabs should match the shoe, like a belt.
Or, to look at it another way, a wardrobe of white-tabbed suspenders allows you to have twice as many for the same amount of money, because you only need one of each pair, instead of two.
Some of Thurston's suspenders come with white tabs as the default. But, for those that don't, they'll happily make the change for no extra charge. They'll do the same for brass adjusters to nickel, or vice-versa.
Thurstons are generally available your choice of two materials: boxcloth or barathea.
Boxcloth is a felt-like material and is the more traditional choice.
I'm not crazy about it because, unlike what we think of today as braces with extra material looped behind the front, between the bottom and the metal adjusters, boxcloth suspenders have on each side just the single strip of material that's visible from the front. That means that the excess material, instead of being concealed in a loop in the back, just dangles below the adjusters, which looks "sloppy" to me.
The only alternative is cutting away the excess (and boxcloth is designed to be cut by the consumer without fraying), but then you limit how much they can be adjusted with trousers of slightly different lengths or rises, as well as risking cutting the suspenders too short and ruining them.
The other material is barathea, which is a roughly 50-50 blend of nylon and cotton. This is what I always choose, and it's what Michael Douglas is pictured wearing at the top of this post, from the first Wall Street movie in 1987. Barathea models are also sized, but are adjustable the more typical way, looped from behind and with a sharp, horizontal line between the material and the leather tabs.
But you might try one of each and see which you like better. Will Boehlke, for example, wears both; according to him, boxcloth is a little more comfortable as it's thicker and has a little more "cushion," while barathea is a little cooler to wear. So he wears boxcloth in the fall and winter, and barathea in the spring and summer.
Your first color should undoubtedly be either red or burgundy, because either will go with absolutely anything.
And, even if you can afford more at once, you should probably just buy one at first to make sure you chose the right size. I'm sure they'll let you exchange them, but why mess with the hassle of exchanging more than one pair?
You could also make do with one, but what fun is that? Besides, each pair will last longer if you get enough for a good rotation. In my opinion, a pretty complete collection would be solids in: red; burgundy; navy; a lighter blue; dark gray; light gray; brown; tan or yellow; Kelly green; olive or bottle green; and pink. This is 11 pair for daily wear. I would also add two formal pair, one in black and one in white. After that, the sky's the limit, like with any collection. Thurston makes plenty of braces in patterns like stripes and dots. A thorough collection is probably 20-25 pair, and an assortment that large is likely to last the rest of your life with fairly even rotation.
Prices are around $70 U.S. per pair, which includes shipping from England.