870=easy question. In your budget (As recommended) an 870 Express. Bass Pro sometimes has the 2-barrel combos (slug and VR barrel) for around $500 new, or at least they did until recently. Otherwise, used...and unlike rifles, I have zero hesitation buying a shotgun used.
Unless you have a real need for a short 20"-24" barrel, the standard versions of these guns have 26" or 28" barrels. There are more hunting applications where longer=better than the other way around, but I do think the turkey barrels are 20" if you can find one.
Once you have your express, treat it well..and it'll return the favour. Neglect it, and blame the finish issues on poor Remington QC. lol I know from first-hand experience that there are 870 Express naysayers out there who treat these guns in a way they'd NEVER treat a Wingmaster...then go on web forums and complain about how 870s are not built the way they used to be. lol They are econo shotguns, but our family express is going strong, and never had a single issue. Looks almost new too. Imagine...dozens of outings, several in wet weather...and ZERO rust. Wow...