Any recommendations for a biggish kit bag, to carry my race gear (shoes, helmet, etc.).

Something which isn’t the ‘floppy cheap stuff’ as I’ve got some like this but perhap has more rigid sides.

I use a plastic tub. Does the job fine.

http://www.duffbag.com/

I have a “ride box” – big plastic box with click closed lid. load it with all ride stuff and sling in van/car. Safe to load with grungies and filthy shoes afterwards too.

needs to be a bag really. I’m just scanning CRc for what they have, something like this? Not sure if needs wheels though.

Ikea blue bag

Mountain Equipment do a bag that is basically the same as the expensive North Face holdall. It’s waterproof-ish and has an internal pocket for wet/dirty stuff.

I’ve had mine a few years now, been slung in and out of the car, on several plane journeys, camping & is still in perfect condition.