I hate washing up. Hate it.
But at the same time I don't want nasty gunky smelly syringes. If I was wealthy I would throw them away after use. But I am not.
So what I do is
A) Designate and label syringes for different uses
Especially anything that has ever been in contact with something mint or menthol will not be used for anything non-mint or non-menthol, no matter how uncharacteristically diligent I am about cleaning.
For plain PG, VG and PGA or DW I have one big 10ml syringe that I use, with a total monster of a needle. I should clean this one more often (I'm telling myself it doesn't really matter...).
For nicotine (though mine is only 36mg/ml) I have one designated 1ml syringe. This one never goes into anything else, and never hosts a needle (but I should clean it more often).
B) I clean the syringes, and the needles (which are way trickier IME), somewhat according to what they have been used for, and how visibly gunky they are. If they are really gunky I first rinse/squirt with warm tapwater, then do vodka. If they aren't visibly gunky I might only do vodka. If they've had some really strong flavouring on them I use some of my precious PGA.
I have been thinking of the rubbing-alcohol I have, but that is only 60% propyl alc, and I'm afraid of taste-residue (probably unnecessarily, I have after all used it to clean things I eat out of).
Since high-strength alcohol is rather expensive (and hard to get where I live), I often use a small jar (one of those miniature jam jars) or a shot glass, or both, and a slop-mug. When I am really focused and diligent about my mixing work, I rinse the syringes and needles in this small jar of alcohol. If they are really gunky or smelly I squirt out the first rinse in the slop mug, if not I re-use the alcohol again and again.
BTW, when it comes to syringes and especially needles, it is hard to say in advance what you will like working with. I didn't at all foresee that I would want needles, but I find them indispensible. Apart from the monster needle for VG (it is 20mm long and 2mm thick!), I have assorted gauges from 14 to 27.
That itty bitty 27G would be fantastic for many things, if it was only longer (I asked for something to help with getting PGA into every nook and cranny of atties to clean them, but haven't used it for that yet), paired with a 1ml or 2ml syringe it gives you fantastic drop control. And it is rather nice to use for dripping when test-
vaping... But an absolute pain to keep clean.