Welcome to the club!
I'll admit, though I've owned a Model 60 for 40 years, it took me a long time to really appreciate it. I was an N-frame snob for a long time. It's really hard not to love that solid feel and smooth, silky action of the big Smiths. They're just not really practical EDC guns, at least not for normal-size folks who don't live in a climate where you need a down parka year-round. I've also got several K-frames I wouldn't part with, but even a 2.5" round-butt K-frame can be a bit hard to hide with a T-shirt & shorts. Enter the Model 60. It can hide out just about anywhere, including your front pants pocket, it packs a solid punch and it's at least as reliable as its bigger cousins. The Airweight variants are so light you can easily forget they're there, too.
My 60 had been my EDC most days since I got a CCW permit, but my daughter, a field archaeologist, was heading out for Indian country (literally) and she wasn't carrying the 9MM I'd given her because of the size and weight, so...off went my faithful 60 with her. Next, I started rooting through the safe for a replacement. After a week or so of the 1911 and the 439 digging me in the short ribs, I was back to the 2.5" Mod. 19, and I was developing a bad case of the Joneses for a J-frame.
After sorting through the LGSs and the online sites for a couple of weeks, I found a Model 36 almost as old as I am for $300 and am once again a happy camper. It's been accumulating holster (pocket) wear since Ike was in the White House, but doesn't appear to have been shot much at all, typical for a J-frame. It's got the skinny sights, old flat latch, and the worn grips have the serial number stamped on the inside of one panel. I've taken those off and put modern grips on, which brings us to that question.
I've tried several options over the years. The OEM S&W grips only virtue, to me, is their small size. I don't find them comfortable to shoot at all. I've tried the newer "banana" S&W grips and didn't find them a huge improvement, not enough to make their bigger profile worthwhile. For some time I used the Pachmayr Compac grips because they were comfortable and made accurate shooting much easier, but they're very bulky. I finally settled on the Hogue Bantam grips. These are extremely small, but surprisingly comfortable. With my mid-to-large mitts there's not enough room to really get my pinkie firmly on them, but they still work well for me. The front of the grip profile is a close match for the old Skip Tyler grip adaptor somebody mentioned and works the same way, giving your fingers enough purchase to keep muzzle flip to a minimum. They leave the backstrap bare, but there's enough rubber on either side to take the sting out of the recoil. I'd recommend you spend $22 on a set and try them. They have a more compact profile than either the Uncle Mike's or the Pachmayr Diamond Pros and you may find they're a good fit.
There's one other change I'd recommend. Wilson Combat, Wolff, Brownell's and Power Custom also market reduced power spring kits for the J-frame. Apex Tactical markets a complete duty/carry kit for the newer internal lock/frame-mounted firing pin guns like yours that also has a new firing pin kit. I've used Wolff before, but I got the Wilson Combat kit for this one. The progressive mainspring and the 13-pound rebound spring lightened and smoothed the double-action pull considerably.
Anyhow, welcome. Take your 60 to the range often, as the J-frame is probably the least user-friendly revolver S&W makes. As the targets some of the crew have posted attest, they're deadly accurate little guns, but they're also what I'd consider an expert's weapon, and getting the most out of them takes dedicated practice that many owners never bother to invest.