I've been using the L-mount system for a while now and honestly, picking just one lens is always about where you want to compromise. I've tried a few of these on my S5II and they all have different strengths for kids sports and travel.

• Sigma 24-70mm f/2.8 DG DN Art L-Mount is basically the gold standard for image quality. The f/2.8 is huge for freezing action at soccer games when the light starts fading, but it is pretty heavy for all-day travel.
• Panasonic Lumix S 24-105mm f/4 Macro OIS might actually be my top pick for you. That extra reach to 105mm is super helpful for getting closer to the action on the field, and it has built-in stabilization.
• Panasonic Lumix S 20-60mm f/3.5-5.6 is amazing for the 20mm wide end when you're sightseeing, but the variable aperture makes it the weakest for sports. If you can find a used copy of the 24-105mm, you'd have money left over for extra batteries or a bag. Lemme know if you need more details on how the AF handles the movement!

Honestly i was kinda disappointed when i first tried shooting soccer with the 24-70mm range. unfortunately the reach just isnt there when the kids move to the other end of the field... you end up cropping so much that you lose all that sharpness anyway. it really wasnt as good as i expected for sports. if you want a real all-rounder that actually fits your budget i would look at the Panasonic Lumix S 24-105mm f/4 Macro OIS. i know people complain about f/4 being slow but the S5II handles high iso so well that you can just crank it up to keep your shutter speed fast for the games. that extra reach to 105mm is a total lifesaver for sports and the macro side of it is actually super fun for travel shots. another one is the Sigma 28-70mm f/2.8 DG DN Contemporary. i had issues with it not being wide enough at 28mm for some tight city shots but it is way lighter than the big Art zoom and fits your budget much better. honestly just pick one and dont overthink it too much... you're gonna have a blast with that camera regardless!

Re: "I've been using the L-mount system for a..."

• I totally agree that picking just one is basically a game of trade-offs. I went through the same dilemma when I first started shooting my nephews' games. I actually jumped on a heavy f/2.8 zoom right away because everyone said it was the gold standard, but honestly? My arms were killing me by halftime. I ended up selling it at a loss a few months later because I just didnt want to carry it on vacation. If you're looking at that $1000 budget, just be careful not to blow it all on a brand new lens that might be too bulky for a casual travel day. I learned the hard way to check the used market first... saved enough on my current setup to grab a decent bag and extra batteries. Also, make sure to think about the reach. Soccer fields are way bigger than they look when you're standing on the sidelines. Sometimes that extra bit of zoom is worth more than a slightly wider aperture, especially if you're shooting during the day anyway. Just something to keep in mind tho before you drop the cash.