Advice: Don't do it. Just play the games that interest you, and forget the rest.
The only problem with SNES/Genesis is that their is significant overlap in their libraries. You'd be playing a couple hundred games twice.
How would you/how did themexicanrunner approach sports games? More modern sports games typically have some semblance of a story mode, but the ones from this era really didn't.
iirc TMR did something like “Win the World Series” or “Win the Super Bowl” since those involved competing a whole season.
I would recommend doing thorough research before just jumping into something like this. Get the full list of all the games you plan to run and lay them all out. Wikipedia is probably the best resource for this. You'll get a good idea of just how much time- at the very least- you can realistically expect to invest in this, and decide whether or not it's worth that time investment. If it is, then I'd recommend putting them all together in a schedule in something like Excel, and plan out at least the first month or two. That should be plenty of time to get the feel of what you're really getting yourself into and after that time, you can re-evaluate whether or not you really want to do this.
I'm about a week and a half into Nanowrimo right now, and it's about the time that people start realizing what exactly it is that they've gotten themselves into. This sounds like a very similar, though much larger scale quest, and I thought I'd give you my opinion while the feeling is still fresh on my mind. That's not to say you shouldn't do it- if it's something you truly want to do, then go for it! but if it's anything like Nanowrimo, there will eventually come a point when it feels like grinding and not very fun, and you'll have to push through it. Talk to anyone Nanowrimo-ing right now and they'll tell you all about it. Cheers, and good luck my friend!
If you're going to do this, which I already advised against, know that TMR may have popularized the idea, but he isn't the only one to do it. A lot of his goals were based on Nintendo Age's attempts at a community beating every NES game: http://nintendoage.com/forum/messageview.cfm?catid=31&threadid=140551 (sample thread) and this list of endings from GameFAQs https://www.gamefaqs.com/nes/916386-nes/faqs/26831
While those are great for NES, I haven't seen the same effort to document Genesis and SNES game endings. There are plenty of on-going "beat the system" library challenges. Some documented in this list: https://docs.google.com/spreadsheets/d/176pFv9a3AJIe14VavJFwFSWdLRK9TZ-5uSy3rFyhoZA (note that most people started up within the first year as TMR, but few dedicated the amount of hours per day, and no other challenges in SNES or Genesis have been completed to date). So, your estimate of 5 years is hardly realistic. In any case, good luck and have fun.