For a 20" barrel, a +3 kit is generally going to match. Sometimes, you can tweak a +3 kit into a +4 with the right internals and shells.
The Remington factory +3 extension is a good kit. I have it and like it. It's a 2-piece design that needs a bracket, so make sure you have the correct one for your barrel spacing. As a 2-piece, it's better for an install-and-done fighting build, rather than a multipurpose gun that you'll be reconfiguring often. Not a ton of internal space, but they're good for +3 with 2.75" shells, and are designed to prioritize reliability. The Remington extensions are a military design, so there is a bayonet end cap that'll stick out past the end of the barrel about a half-inch. This won't hurt anything, but some folks don't like the way that looks.
S&J Hardware makes some really great single-piece extensions. I've been reviewing one of their MK II +2 kits, and I'm really impressed. They say the +3 version is designed to line up with a 20" 870 barrel, you can email them if you want to know the exact length. They're not the cheapest option, but they're really tough and well-designed. Excellent reliability and good internal space.
Choate's +3 is another single-piece kit. I have one here for evaluation, but I haven't really played with it much. Seems to have potential, though. I can say that it'll line up with a 20" barrel nicely, and it has good internal space. You can tweak this one into a +4 if your shells aren't crimped too long. It's more of a budget kit, which isn't necessarily a bad thing depending on your needs, but it's not built as heavily as some other options.
Wilson Combat extensions are really great budget kits; tough, reliable, with some nice extras and an array of options for sling attachment points to choose from. I normally recommend these for budget builds because they're really affordable and all you give up for the low cost is a bit of refinement and some minor side features, but they're only made in +1 and +2 versions. Still might be worth considering, unless you're really set on a full-length mag (though keep in mind that a longer tube with more shells will also add weight).
I haven't used the Nordic extensions personally. They're modular all-aluminum kits, and are really popular with competition guys. May not be the best choice if your 870 is going to see real rough use, since they don't use a really high-strength aluminum alloy, but they should work fine for HD. Like a lot of high-end competition gear, they're on the expensive end of the scale.