"Sleek and modern" can be approached many ways. My benchmark for sleek and modern has pretty much always been Bang & Olufsen. Many frequenting this forum disparage the brand, but it usually has nothing to do with their styling or build quality, but value-for-money and their design and integration of their products. As you probably know, they are expensive, but they look great. They are also the kind of brand that integrates their products. Their speakers are usually active and wireless, so the amplifier choice is made for you. Most buyers of their speakers are using their whole system, sources and all. I am sure you could just use their speakers with a sub and choose your own components.
If you want box monitors, there are lots to choose from many brands. A decent place to start might be the Q Acoustics Concept 300 with the white/oak finish and the Tensegrity stands. I have a pair of Amphion Argon 3S in Full White on matte black metal stands. The colorway is "modern" and the finish free of distracting ornament. In a lighter room, they don't appear large and their performance is excellent (with a sub.) The cost is above your stated budget. One option that is not, however, is the Q Acoustics M20 active, which IMHO is an example of remarkable design and engineering on a budget. It is available in white with a grey grille. It really is an excellent example of the positive directions that company is capable of moving. In fact, before you buy, you really should hear a pair just to have a basis for comparison.
If you are looking for very modern, look at the Eclipse TD510TZ Mk2. You’ll need a sub.