We are landing at LGW (Gatwick) in London at 8:00 am & want to take the tunnel train to Paris that morning. Not sure how much time to schedule for baggage pick-up & transportation to Waterloo. Worried about missing train if I buy tickets too close to arrival time. Thanks

It takes just over an hour and you have either to change trains twice or get the tube from Victoria to Waterloo.
I checked to see if going to Ashford International in Kent was quicker, but it isn't.

You also need to check in at waterloo about 30 mins before departure.

I wouldn't even think of booking before midday - and I'd probably be so worried I'd stay in London overnight and go the next day

w/ an 0800 arrival you won't be totally safe booking any morning Eurostar. You could get to Victoria or London Bridge by about 1000. But it is also possible you won't be there until later. Then you have to take a train/tube/taxi on to Waterloo.

I would feel OK w/ a train just after 1 p.m. - that should be fine - but if your flight is late all bets are off.

What about a mid-afternoon train- 3, 4? That way you can take your time getting to the station, maybe even have lunch in town. If your flight is even the least bit late, you are going to have to run through London, and that's very stressful.