You didn't specify a budget, so let's go wild!
A
Gennaker is not really a downwind sail, it's for a beam reach, although the term is often used interchangeably with asymmetric (spinnaker). If you want to go dead downwind, a (symmetric) spinnaker will give you the best performance, although not easiest to handle short-handed. You can fly it freely without a pole, but that limits it to really just 180° and not much else. With a pole, it can be used at a wider range of angles, but not as far down as an asymmetric. Gybing a poled out spinnaker is not everyones idea of a fun time and can lead to bent poles and damaged relationships. A Parasailor is just a gimmicked out spinnaker that is a bit easier to handle and more forgiving (also pretty pricey and usually comes with a snuffer). It has a "tongue" that helps it fly and a gap that reduces the risk of broaching, as it basically lets some air out of the sail.
An asymmetric is probably the most popular option for cruisers at the moment, especially if flown on a retractable/removable bowsprit with a top-down furler. Very easy to handle that way. Also the most costly option. The sail is left on the flexible torsion rope and simply stuffed down the forehatch (top and bottom ends last), complete with the endless line furler and everything. To
deploy it, attach a halyard at the top, the foot to the bowsprit and raise the whole sausage up, clip the furling line in and unfurl. A cheaper option than the top-down furler is the ATN tacker or a fitting somewhere on the bow ahead of the forestay, plus a snuffer. Slightly more difficult to gybe this way, and many prefer to snuff it, gybe and let it out again. With an asymmetric you typically don't sail dead downwind, but gybe downwind for maximum VMG.
And don't forget the old-fashioned option of simply poling out the Genoa (with a whisker pole, typically a bit shorter than the foot of the sail, but longer than a spinnaker pole, which is restricted in length because it must be able to dip under the forestay). The main goes out the other side with a preventer on, giving you a "barn doors" setup. I've played with this setup on my boat and found it working surprisingly well (my 2001 Bavaria has the older type rig, with large 150% Genoa - won't work as well on the newer blade jib rigs). As budget is an issue for me, I've decided to go with that, and am currently shopping for a telescoping pole (3.9 to 5.9m long or thereabouts).
You can try this setup for yourself without any further equipment in light airs, by steering dead downwind (helm must pay some attention here), gybing the main to the other side of the genoa (use a preventer!). The Genoa will stay filled on its own without a pole (see photo from my boat). You can then grab your telescoping boat hook and push out the clew of the Genoa to see what difference a pole would make (and work out how long yours ought to be - although measuring the foot of the sale will also give you an idea). Without a pole this cannot be left unattended, but with a pole the setup is much more stable. Performance at least on my boat was surprisingly good.
Finally there's the even older fashioned option of flying to Genoas/Jibs from a single or twin forestays. Haven't seen this setup in a while, but it used to be all the rage in the days of Susan and Eric Hiscock