I've done this journey a fair few times, usually with roll aboard but sometimes also with a checked bag, most often arriving back from BDA and showering in the arrivals facility at the Sofitel, hence taking the train ~8am. Yes, it's busy - be prepared to stand, at least as far as East Croydon. Seeing as the First Capital Connect service links two airports via central London, the carriages do make greater provision for luggage (certainly compared to another company's commuter trains I take on a different route to/from London 'every' day). The only time it's been unbearable is at times of irrops (flooded track a while back wreaked havoc). A cab into central Lon at that time would be far more frustrating IMO than ~30 mins on a busy train.

There's a wide variety of fares and routes but the £9.90 option (or whatever it goes up to from 2 Jan, if appropriate) is the one to get. I once took a Southern service but that was tortuously slow and best avoided, again IMO.