I'm currently using a Trijicon Reflex II, but I also want to get in some time with both my EOTech 450 as well as with my DocterSight (using a Burris FastFire Picatinny mount), to see which one fits me better. Why an optic on a HD shotgun? because I'm very strongly left-eye dominant, and I want to shoot with both eyes open: neither a bead nor ironsights will allow me to do this.
You can "date" my purchases by the sights. All are c. late-90s, early 2K. The Trijicon is still going strong, and the reason why I like it is because it's a "no-brainer" sight - there's nothing I need to adjust: just pick her up and go. The Docter's battery lasts for years in a dimmed mode, when the protective cap is over its body, and I really like the fact that it is so small. Perhaps, when the tritium in the Trijicon finally gives up the ghost, I'll go for a miniature Trijicon? The EOTech again has batteries that will last years, but it does take a push of a button - nevertheless, given that my intended use of the shotgun is as a "bunker gun" (in our safe-room, with the family behind me), that should not be much of a concern. Of the three, the EOTech is definitely the easiest to acquire the reticle.
The light on my 870 is a dedicated Surefire 618LM forend. That's a pretty penny, so I don't think you'll want to go that route - but there are a lot of choices available for you to take, even with budget among the leading concerns.
You can either get one of those small pieces of rail and screw it in to your forend or, alternatively, there's plenty of barrel/magazine-tube "clamp" devices available - ranging from those that come with a small section of rail to ones that specifically fit 1" tube-diameter handheld flashlights. There's also options like what LongRider showed, which have integral vertical foregrips.