You can make your own with paper easily.
- Take a standard sheet of paper and put the grid on it manually. Graph paper will make this step easier.
- Once you have one page with the proper gridlines, photocopy as many as you need for your mat (I'd estimate somewhere around 15 or 20).
- Match the gridlines up and tape the pages together.
- Now get some clear contact paper and place it adhesive side up on a table.
- Lay down your gridded paper on the contact paper so they make a battlemat of what ever size you desire. For more durability, laminate the back side too.
The clear contact paper works well with wet-erase markers (I've never tried dry-erase markers).
As for size, I personally just use 2 sheets wide by 2 sheets tall (of 8-1/2 X 11 inch paper), so I guess that's something near 17X22.
My group uses a private Google+ community to organise the games, and G+ alongside Roll20 to play the games. We play entirely online on a weekly basis, mainly because we're all about the same age and have small children and families, so it's difficult to get together for a face to face game.
For D&D 5th Ed you're pretty spoiled for choice, but when it all boils down the best two options are this:
Roll20, either in conjunction with G+ or on it's own. You can create an account and run your campaign through it for free, and the biggest pro (in my opinion) was the ease of use when it integrates with G+. Most everyone has a google account these days, so they also have a G+ account whether they know it or not. Once you've created your game in Roll20, you can choose to launch it in a g+ hangout.
Once you've done that for the first time, whenever you launch a G+ hangout the Roll20 app will be present, and you can launch it and select your campaign from within the hangout. Running the game each week becomes as simple as scheduling a G+ hangout event and showing up - the players don't even need Roll20 accounts, they just click the hangout invite link and game on. The D&D 5e character sheet for Roll20 seems pretty excellent too, with some dice rolling automation built into it. We're taking it for a test run soon hopefully.
The other main option right now, though it can get pricy, is Fantasy Grounds. It's not as simple for the players as Roll20 (which is, as i've said, just a link click), but if they're willing to install the program (available on Steam now as well), Fantasy Grounds is now the official online tool for D&D 5th, in partnership with Wizards of the Coast. It has excellent integration with the rules system and character sheets, as well as supporting hero lab. Some friends of mine swear by it, though it is a bit more complicated to get set up and running.
Both solutions support full voice, and I know Roll20 supports full video both in the app itself and through hangouts, as well as an online tabletop for maps, images, handouts and whatever else you like. This made it a lot easier for us to retain that "social tabletop" feeling, despite playing entirely remote. Using a large enough screen and a good set of speakers and microphone, you could play partial remote (with only a few players remote) or even with everyone in the room and disabling the voice and video altogether if you wanted.
Either way, if you do plan on getting in to running your games online through virtual tabletops, Google+ is your friend! There is a massive community of people there who will be more than happy to lend any assistance required.
Personally, I run a community geared at assisting people to set up, run or find games in the asia-pacific time zones. You can find it here: https://plus.google.com/u/0/communities/100566740249118526694
For other timezones, such as the American zones, a great place to start is here: https://plus.google.com/u/0/communities/107422815813208456454 It's an excellent community filled with friendly people.
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For remote play at our table, we use a camera that is stuck on a microphone-boom-arm that can be rotated by 360°. We found out that we prefer it to have our rest position at about 45°, instead of top-down because the top-down angle creates nausea for some of our players, and it simulates sitting at a table.
We use a 19 by 19 go-board with numbered and lettered tiles, so if a player wants to move they say:
There are different kinds of boom-arms that you can use. We tested for a while. We now use one with a tripod stand as it is the most stable while remaining flexible as opposed to the mountable-holder that we initially fixed to our gaming-table.
For indicating features, we use a mix of miniatures that were part of the 2002 D&D boardgame by Hasbro and cardboard printouts that create terrain objects by sliding them together at a 90° angle with little plastic sockets, so they don't topple over.