A klein is a tough 'cross conversion. They tend to run pretty tight in the rear triangle, so you will be very limited in what tires you can run. Internal cable routing is not great for cross, and obviously you can’t add cantis on to the frame. I wouldn’t worry too much about the geometry, though; cross bikes are pretty tight and steep these days.
If you think even for a second that you will stick with cross, don’t pump money into a “conversion.” Go out to a 'cross clinic or practice session (or 2, or 3…) on your road bike, and if you like it, figure out a way to buy a 'cross bike. Or use a mountain bike.
There are many used cross bikes available (heck, I have a couple for sale myself,) and you can probably get a 'cross bike for not much more than you would spend incrementally piecing together a makeshift rig. The cheapest POS cross bike you can buy is going to be better than any roadbike conversion you come up with.
I lead the cross clinics in Seattle, and out of 500 + riders I personally coached this season, I can count on one hand the number of riders who used conversion bikes. I think all but 1 or 2 of those finagled a cross rig of some sort by seasons end (lots of people used mountain bikes.)
Big thumbs down on the Vittoria tire recomendation. They are a stopgap at best - they MIGHT fit on your bike, in which case you can use them to check out cross (on your roadbike) to see if you like it. Trying to race on them would be incredibly frustrating. Especially for a beginner, watching people ride around you while you pick yourself up off the grass because your tires suck is no fun - and make no mistake about it, the Vittorias do suck (I remember paying insane money for Clement tires, hand carried over from Europe, just so I wouldn’t have to ride Vittorias, which were all that was available back in the day. Wiejak schooled everyone at nat’s one year in part because he had Dugast 38’s and most of the field were stuck with crap…) The Ritchey semi-slicks are yards ahead of the Vittorias, and they will fit on your bike if the Vittorias will ( If anyone really wants some of the icky Vittorias, I am pretty sure I have a couple of pair in the storage shed…)
The parts spec on your bike sounds just fine. You could switch most of it over to a cross frame with no problem. All you would need would be new brakes and tires (probably…)
Pedal choice for cross is pretty much personal preference, with the exception being that I do not know of a single high-caliber cross rider that has been able to make Frogs work for cross. They are pretty much the only good mtn. bike system that does not convert well. The vast majority of world-class cross riders (read as: european) use Shimano pedals. Time has been the favorite in the US for several years, but many Elite US riders have switched to Crank Bros. I am currently using the Crank Bros Candy SL pedals, and I would buy them if they didn’t give them to me. I prefer them to the Atac pedals, but ymmv.