If you and your players really want to turn DnD into an economy simulator, you can certainly do that. I personally handle things like castles and mines and guilds and stuff that the players are involved with by having them dictate major directions in their operation (my thieves guild is going to be focused on gathering information via beggars), and maybe place a few trusted NPC's into key positions to handle the day-to-day stuff. Income and funds are assumed to be plowed back into the operation.
As for rewards to having such a thing, it really depends on the time scale of the campaign. If it's part of published AP where they are going from 1-15+ within about a year of game time, then there's very little benefit beyond access to standard goods and maybe some political influence. Something like a mine would honestly take years of investment to even start making money, assuming normal economical restrictions are in place. I mean, you need places to store the silver, housing for the workers (unless your mine is conveniently located near a major town), transportation for the silver, trusted guards and manager-types to keep the whole thing from imploding as soon as you leave, and the political connections to establish contracts for the product so that you're not treading water with small-scale transactions.
That stuff isn't cheap, and it's incredibly unlikely that the players would stumble on a "turn-key" operation that is somehow not being inherited *and* isn't simply getting possessed by the local lord or king or whatever. But assuming there's justification in place (maybe a PC is the inheritor, or they managed to blackmail the local lord), they still have to deal with a myriad of infrastructure and political investments.
Basically, the more detailed you try and make the system, the less believable it becomes that the characters would be involved. So just focus on the broad aspects, and don't let players start counting coppers like the mine is a debit card. It could very well make them all wealthy at some point, but it's not likely going to happen until after their adventuring career. Until that time, it can serve as a great plot device and starting point for political intrigue or a "we dug too deep" adventure.
