A shotgun mic will be better in a quiet location - but you initially indicated the court, players, bouncing balls would be around, hence my suggestion of the handheld.
Again, mimic what you see on TV.
During an interview with a talking head and there is not a lot of background noise, a lavaliere can be used. Note the location of where it is clipped on. About 4 inches away from the audio source. (Review: The hand-held dynamic mic was "in their face".)
Good UHF multi-channel wireless lavs can be expensive. A thin wire connects the clipped-on mic element to a battery powered body-pack transmitter. The audio signal is transmitted wirelessly to a base station. The base station plugs into the XLR adapter or the camcorder. Some base stations are large and require AC power. Some base stations are small (camera-mountable) and are battery powered. I like/own/use the Sennheiser G3 systems with portable base station. I got the add-on module for wired mic conversion (the wired mic can be wireless).
When are shotgun mics used? When used properly, in a studio when it is *very* quiet or during a film shoot when seeing a clip-on mic on the talent is out of place or during an impromptu interview when there was no time to set up dynamic mics at a podium AND there is not much background noise OR, there is no other choice. Shotgun mics do have a directional pick-up pattern, but only the most expensive ones include "side mics" that are used to reject audio from the sides (or behind the front-facing mic.) The affordable shotgun mics generally rely on a relatively quiet background with just the mic's pick-up pattern (get what's in front of the mic). Good shotgun mics can very effectively focus their audio pick up, but all will pick up background noise. ("QUIET ON THE SET!").
Again, mimic what we see on TV... a shotgun mic at the end of a boom pole held by an audio person (separate from the camera person). The long shielded cable connects with XLR connectors connects the mic to the camcorder - or, a portable audio mixer or, preferably, an external audio recording device (Fostex, Zoom H4 - lots of others) and the audio is synch'd with the video during editing. And the shotgun mic is wearing a "fuzzy" or "dead cat" or zeppelin to eliminate wind noise.
There is occasional use of a camera mounted shotgun mic if the mic is no more than about 4 feet away from the audio source. Some folks think a shotgun mic at the back of a room will pick up just the audio in front of the mic (and fail to take into account that the space/noise between the mic and the audio source at the front of the room will be ignored and that's just impossible. I know this is not your case, but just making the point that a shotgun mic cannot magically eliminate ambient audio). The closer the mic element is to the person speaking (the audio source), for interviews, the better the audio will be.
I have not used the Sony ECM-HW2. Should it work? Sure. BlueTooth is a fine technology. The ECM-HW2 can be used *only* by Sony products with a Sony-proprietary AIS (Advanced or Active Interface Shoe). The ECM-AW3 can be used with any 3.5mm audio input. I have not used this, either. There are wired lavs, too. They, like other mics, are all over the map regarding connectivity, pricing and quality...