Pat I don't want to get into a debate, but I would definitely not label kettlebell sport as soft style (witness the video above).
As far as training for kettlebell spor, the way Valery recommends (I have done his certs and competed in my first kettlebell sport meet this year) is one set of jerks, one set of snatches done 5-6 days a week.
You would start at 5 minutes for the jerk, working at 6 rpm and then build the time up to 7 minutes. Once you can do that, up the rpm and drop back to 5 minutes.
Similar for snatch. 6 minute sets to start, one hand change, start around 12-14 rpm and build up to 16-18 rpm. Then gradually increase to 8 minutes.
Once you have the basic technique down and can do a decent volume, you would add in heavy (4-12 kg heavier than your working weight) one arm jerks (one set of 10-20 per hand) and swings (1-2 sets of up to 50 reps per hand).
If you are doing long cycle, you would replace the jerks with long cycle, and possibly the snatches with cleans - if you need the extra work.
I'd highly recommend going to the WKC store and downloading Valery's video "An Introduction to Kettlebells". It covers a lot of technique points that are important for safe lifting. If you can get a WKC coach in your area for a couple of sessions, that would help tremendously too.
Also check out Scott Shetler's book "Kettlebells for Sport and Fitness", it outlines a lot of training templates, including modified Westside and 5/3/1 type programs with kettlebells as well as kettlebell sport templates.
As far as 'regular' strength work, I was relatively strong, not earth shattering, but deadlifted 229 kg at 87 kg and squatted 150 kg before starting kettlebell sport training, but it's a different ball game with the 'bells.
Your limiting factor isn't strength if you come from a weights background, it's technique, speed and endurance in varying degrees of each. I work solely with the 'bells now and you'll find that is the fastest way to make progress, whether you want to compete or not.
Of course, if you are training solely for enjoyment and fitness, and you enjoy barbell training, by all means, include it, but most top end kettlebell sport lifters do little to no barbell training (*outside of 'jumping squats' to build the legs for jerks).
Remember the joints take a longer time to adapt to the high volume of lifting, so don't be in a rush.
EDIT: extra info, both times