Gatewick Express

Firstly it's Gatwick, not Gatewick.
The Gatwick Express is an expensive and overhyped branded service which will get you to Victoria just a few minutes quicker than the normal Southern train services for a lot more money.
The sensible thing to do is to take a regular Southern train destination Victoria showing East Croydon as its first stop. You don't need a ticket but can use a contactless card or phone or smart watch pay - that's the cheapest way to do it.
Don't whatever you do succumb to any form of road transport - the journey into central London is purgatory and will take much, much longer than the train.

The train station is right there at the airport and clearly marked. You won't have any difficulties finding it. You can either use a contactless card or buy a ticket at the machine at the station. Just take the regular train.

Use the southern trains.pay by contactless lets you bypass the line at the ticket machines. When you go down to the platform walk down a bit. People tend to cluster right where the escalator leaves you. So fewer people further along the platform gives you a better chance of snagging a seat and luggage rack space.

I would normally go with the consensus and suggest the Southern train. However I'm a bit concerned about "I will be bringing a fairly large suitcase", and while the Southern train will accommodate normal cabin baggage and normal checked baggage I wonder if "fairly large" might be better suited to the Gatwick Express's capacious luggage areas...

So how large is fairly large? I've seen some big ones in my days....

Thank everyone for their informed and helpful advice. I maybe should have explained a little bit more about myself. I’m 75, not the strongest guy around, and traveling on my own, and like to anticipate any issues I may have before I go. My suitcase isn’t extraordinarily large but not carry-on size either – it’s probably a large checked-baggage size and will weigh over 40 pounds. When I’ve traveled in the past, I’ve struggled lifting it over my head to put it in a high or overhead bin, or lugging it up stairs. I’m not in any way rich but I would rather pay a little more for convenience if it would make it easier for me. Also, and perhaps this is just me more than anything else, when I was in the Netherlands last year and I tried to use my contactless credit card a few times and sometimes in didn’t work when I was hurrying to reach a train, so at the time I said to myself – “next time, buy in advance.” And I would like to keep those tickets on my phone.