A stock rear shock will provide the level of precision and adjustment you are likely looking for. If spending the money for a quality rear shock, it makes sense to balance the bike with the front end receiving springs, good oil, and a freshening up. If you have a bank roll to kill, front fork rebuild with valving and adjusters would round off a suspension upgrade without a full fork set replacement.
I've used Ohlins and Fox, and both work well, though I did love ohlins on my K2 GSXR 1000. Fox are sold out of RMR racing in BC, and should be significantly cheaper than a new ohlins. for Ohlins, that generation of GSXR uses the old (and good) S46 series shock, not the TTX. Not sure if the S46PR1C2LS for a K4-K5 will fit the K1-K3. Probably best to double check. Elka is another option, but if its only $1-200 more for Ohlins, get the better hardware.