How to get started?

[KalSaj]

Wow, a lot of good advice in this thread!

The question [...] "Is there a martial art that comes with a significant downside if my real goal is lightsaber combat". It sounds like the answer to that is "no"

To add in my two cents and a different perspective, there really isn't a downside. It's more like "how will a particular martial art shade your perspective on saber combat?". Obviously Kendo/Kenjutsu will give you a direct link to sword combat. An Iaido practitioner might really dig blade deflection and/or the complex bladework required for two sabers. A Karate/TaeKwonDo user may focus more on their rooted stances and strikes using rotation as leverage. A Wing Chun user may look at minimizing the energy expenditure and deflecting/trapping the opponent's blade using their own energy against them. And, of course, all of these promote proprioception (body awareness) which is critical.

The important thing, I think, if you're using a martial art to inform your saber work, is not to let the scope of your martial art limit your saberwork. Yeah, Makashi derives heavily from fencing. You could live a long a happy Makashi-life using only fencing-derived moves. That doesn't mean you can't take the principle of the straight punch from Wing Chun and add it in (you could argue the straight punch is the open-hand equivalent of the shiak, the thurst, in saber combat and can be implemented using the same stances/timing as a sword thrust might).

"Research your own experience; absorb what is useful, reject what is useless and add what is essentially your own."

[Master Nero Attoru]

Speaking as a former student of martial arts, there really is not what you would call a "useless system". Some are better than others in certain situations, but the more styles you practice, the more you'll know what to do given any kind of threat.

Sure, the kinetics of karate may not translate particularly well to saber combat (as karate is focused on empty hand striking, although certain dojos do offer weapons training), most all martial arts are more than just combat. It's more of a mindset. Martial arts training also instills other, nonphysical skills, including threat recognition, faster responses, and increased reaction times, all of which can translate into other areas outside of combat.

If you're set that you can't make the saber specific classes, get into anything. You won't be disappointed.

This is a good summary, although I'll add one caveat - your teacher matters greatly.  Martial arts systems developed in reaction to their own individual circumstances, so they all typically have something to offer.  However, there's a large difference between a proper school with a good teacher, and a poor school with someone unqualified to teach.  The latter can result in improper technique, and in some cases, severe injury.  As much as possible, I recommend doing your research on a program before jumping right in.

You're always welcome to ask those of us in the community as well!