Baitcaster / level wind reels are the norm for most folks and I rarely see anyone using a spinning reel since line twist can become a major issue over time, especially for those the reel against fish when not gaining line. When I first started Kokanee fishing I used spinning reels since I was converting over from trout fishing.
The reels I like the most right now are the Tica Caiman Series reels, CM150 or the slightly less expensive CT150 models. I also have a number of Abu Garcia 4500 C4 series reels that work fine as well, I prefer the C4 series over the C3 (more ball bearings and smoother). The key for any of these is a smooth drag system. The Tica's are great in that you release one screw (and it stays in place and does not fall out) and then twist the reel and it is open for you to do any work or maintenance.
As for swivels to the dodgers I'm a big fan of very high quality ball bearing swivels just in case you get a lure combo out of control then the swivel may be able to keep your line from twisting. The swivels from Sampo are the ones I use. They are not cheap but I trust them and then never have failed. Here's a link to them:
http://www.sampoinc.com/sa_spr_locksnap.htm