Gatwick to Waterloo for Eurostar
 

We will arrive LGW at 6:30 AM on a Wednesday, and our train departs Waterloo at 10:40 AM.(I really wanted to allow plenty of time, as there can always be unanticipated delays)

I've read the previous messages on the subject, so I know there are a couple of options, but for those that know this route, which do you think would work best for travel at this peak AM time? We will each have 1 26" rolling case and one piece of hand luggage. We're pretty adept at making our way around, but we will be tired from our trip across the pond.
I know we'll need to get some pounds for taxi, coffee, newspaper, but we will not be spending any time in London other than to/from the train station/airport, so I'm not sure just how much cash I should get. Thanks for your ideas, Barb

Call me a lazy wastrel, but given that there are two of you and you'll each have a full size suitcase, I would say take the express to Victoria and a taxi to Waterloo.
Although it's more expensive, you get to experience a "real" London taxi ride (if you've never done one), you'll get door to door service (well, train station door to train station door service), the route is kind of nice, you'll go past the Houses of Parliament and over the Thames with a good view of the London Eye and you'll be dropped off close to Eurostar check in.
Or you could simply arrange for a car service to take you from Gatwick to Waterloo, which I guess you could prepay with your credit card, so you'd need fewer ££.
Several car services have been recommended here...Swiss Cottage, Just Airports, etc.
By the way, after you go through Eurostar check-in at Waterloo, there's a bagel place and a Coffee Costa, so you could get coffee and a snack there. Don't get coffee before you check in unless you plan to finish it first as you can't take any open beverages through Eurostar check-in.

I did this with my husband, teenage son and 70 year old parents. We all had one rolling bag and a smaller one. Here's what we did with no problems:

Landed at Gatwick, went thru customs in a flash and found the connection to the Thameslink train in the South terminal of the airport. We switched trains at the London Bridge stop and went on to Waterloo East..up a few ramps and we were at Waterloo International train station.

The London Bridge route is fine except during rush hours when trains will be packed and you'll have to navigate a mobbed station at London Bridge to board an already full train to Waterloo.
In off peak it's an easy good way to Gatwick-waterloo. But BTike's Gatwick Express/taxi is by far the quickest and best with luggage at this time of day.
Personally i would have put an extra two hours in before the Waterloo trains in case planes are late - must check in on Eurostar 40-45 minutes ahead of time now i guess due to enhanced security i guess.
there can also be long queues at Customs at Gatwick - land at 6:30, get thru customs by 7:30 at best, walk to train, wait for train 30 more mins; an hour to get to Waterloo means if things go normally you'll be there about 9am have to board Eurostar by 10am - leaves only an hour for plane to be delayed - hope Eurostar ticket is refundable.

On your timetable, the Gatwick Express/taxi combination is the only one that makes sense.

Getting a car into town, leaving LGW at 0730-0800 on a weekday, is horrible. But not aquite as horrible as the Southern or Thameslink trains will be.