As far as I know, none of the 'normal' (ie not Gatwick Express) trains sell anything other than Anytime tickets, so you shouldn't have an issue.

On the grounds you want a paper ticket for the 2-4-1 offers, and aren't interested in the saving using Oyster/contactless, the one-way price will be around £10 (it'll vary a bit depending on which London station you travel into). Depending on the location of your hotel, you might want to consider Southern services into London Bridge or Thameslink services into St Pancras or Blackfriars (which is generally quicker due to less stops). For Southern services, it's actually cheaper, I think, to buy two singles. For Thameslink the return is ever so slightly cheaper compared to two singles, but not enough given the loss of flexibility to swap stations at the last minute if there are issues on the day to justify it.

Incidentally, the National Rail website doesn't do a good job of listing all services from Gatwick - for Blackfriars times, you may need to select the station specifically.

The restriction then is that you must travel on the operator on your ticket - so you can't use a Southern service if you've bought an Anytime Thameslink ticket, and vice versa. As the services more-or-less overlap each other on departure times, this isn't much of a hardship though.

Because these are Anytime tickets, you can buy in advance or on-the-day - the price won't change. If you're certain of your day of travel, I'd buy in advance purely to avoid any potential queues at ticket offices - either you'll get the option to print your own ticket, or you'll get a reference number to collect at any ticket machine (doesn't have to be at your departure station).