David Walser
I'll try to address each of your questions in turn:

1. What's the minimal set of gauges I need to turn these? A parting tool and a spindle roughing gouge should be able to handle these simple shapes. I'd recommend a spindle roughing gouge about 3/4" in size. (I've included a link to an example of the type of gouge I mean.) The gouges are available from a number of vendors at a variety of price points. A 3/4" skew would (in the right hands) leave a better finish than that obtained from a spindle roughing gouge, but a spindle roughing gouge will give you a very good finish if you're careful. After sanding, no one would be able to tell the difference.

2. The pieces in the photo are made of oak. I presume I should pick that or another type of hardwood rather than pine or something similar that's soft. Other than maple, what other common wood types would you choose? Do you think poplar would be too soft? I think poplar would be too soft as would pine or fir. I'd suggest, in addition to red oak and maple, white oak and ash. All are readily available at reasonable prices. I would assume that it would be acceptable to glue up blanks of appropriate thickness. This would let you use generally less expensive thinner stock.

3. Do you think for a novice like me, it would be easier to turn each target piece separately, or turn one long one which I would simply later cut into 20cm pieces? Even though the shape is a simple cylinder, I do need the targets to be the same size. A lot depends on the size of your lathe. It might be simpler and easier to do two or three at a time. A simple cylinder (as opposed to a taper) is not too difficult to obtain as long as you have a good set of calipers and remember to measure often.

4. Looks like the most complicated part are the long tapered bats. Is there a good resource online that would describe how to turn these? The AAW, as part of their FUNdamentals program has a brief video showing how to turn tapers and cylinders. If you are an AAW member (or know a member who will let you see the videos on the member's computer), the videos should get you started.

If not, do as was suggested in the prior response. After you've turned your blank round, carefully lay out the dimensions of the bat. Mark the center and end points of the bat with a pencil. Mark several points in between the center and end points with a pencil. Then, set your calipers for just slightly more than the appropriate diameter at the first of the marked locations (it doesn't matter which one) and use your parting tool to cut the blank down to that diameter -- measuring often. Once the calipers just barely slip over the blank, re-mark that location with a dark pencil line. After you've used the parting tool to set the diameter at each location, use your spindle roughing gouge to "connect the dots" -- being sure to leave your pencil marks at each marked location! After you've connected the dots, you'll have your bat almost completed. It should be just slightly larger than your desired finish diameter along it's full length. A light pass or two along the length of the bat with your spindle roughing gouge and a little sanding should be all that's required (other than cutting the blank to final length) before adding your finish of choice.

Good luck!