The advice these days is for a clean line - so no handles etc., or at least not that can't be easily removed. Also the base of the bag, and the way the rope joins to it, should be suitable to have a small loop (to attach a carabiner when necessary) without that loop being able to twist and crush fingers is someone does hold it by the loop.
That also means no integrated straps or dangly buckles when detached, but for rafting, canoeing, and SUP there are bags that leave the strap cleanly behind. For WW kayaking they're unnecessary as they'll get in the way of a spray deck. Similarly bag fastenings shouldn't be fiddly - of course you don't want the rope falling out, but neither do you want to fail to fully undo one of two fastenings and throw short. Mine had a drawstring (possibly made of shock cord) as well as Veclro. Now it just has Velcro because the drawstring got in the way for no real benefit.
You need to decide on what the line is mainly for - 8mm rope is good for rescuing swimmers, but if you're going to be recovering boats using force-multiplying techniques it's not really strong enough. Note that thicker lines are easier to hold, and Spectra tends to be used precisely to be thin (and therefore light). For grabbing the line (and you should assume that the line, not the bag, is being grabbed) 8mm is good, but some Spectra lines are only 1/4" (6mm) - so if you go for Spectra, go for 10mm (3/8"), which is then a recovery line.
In a group, it might be appropriate to carry mainly light lines, with one or two 11mm lines. In some cases, some paddlers may carry both. If carrying both, the swimmer-rescue line should be nice and accessible because you'll grab it often, for example when inspecting from the bank. The heavier recovery line can be tucked away as there's less urgency in setting up to recover kit.
Your line should be sized so that you can throw it accurately. There's no point having 25m of 11mm line if you can't hit a paddler more than 15m away reliably. Training will help here.
Obviously the line should be easily visible, but modern lines all seem to be bright colours.
Personally I rather like the flattened rope in my throw bag, but it's not a major factor. So, for the fairly narrow rivers in the UK, I carry a 20m rescue bag - I can aim that well at its full length, and it fits in an accessible place in my boat. But I know there will be both longer and heavier bags in the group. The club I paddle with trains everyone in throwline use, so most paddlers, not just leaders, will be carrying one, and some of the ones that can be borrowed from the club are among the biggest you can get. I carry a 5m webbing sling for lifting and lowering boats on banks, so don't use my throwline for that.
This article from Palm is worth reading, though it's heavily geared towards their own products.