G305 has been my go-to recommendation for a while now.
It's small and light, with a great sensor. It runs off a single AA battery, and you can swap that out for a AAA with an adapter if you want to shave off even more weight.
Unlike most gaming mice, it's also available in white rather than black, and doesn't look too far removed from a standard office mouse rather than a Michael Bay Transformer.
I recommend avoiding rechargeable mice unless it comes with a dock. Having to remember to plug in the mouse all the time, or using it wired while it charges, is awful.
With a mouse like the G305 you can use Eneloops and keep a spare battery in the charger at all times.
Logitech G602 is really good and not super expensive.
This is a big and heavy mouse (even with one battery) that has an old sensor and polls at 500Hz.
It's not a
bad mouse - I really like the side-button layout - but it's not one that I'd recommend someone buy now; at least not for gaming.