I don't know how to say this without sound patronizing or dismissive or some sort of negative, but ...

I'm wildly pessimistic about the chances of someone walking across country who has no long distance hiking experience. The ADT is indeed the best there is in terms of a path across the country, but very few have done it, and I rather imagine that the few that have didn't start from with a low experience base. Asking about basic tent stuff suggests little or no experience at this.

You can certainly learn long distance backpacking "as you go", but best is to do so in a more realistic setting where others can help you out. I'd suggest trying to hike a sizeable portion of the PCT or the AT. This particular year, the water situation for those starting the PCT in April/May (from the Mexican border) is tougher than usual, but in general best is to start more or less "with the crowd" and thus have a lot of ready mentors as you figure this stuff out as you go along.

I'm not saying that you can't make it. I'm saying that I agree with those that suggest it's highly unlikely that you will, at least if your intention is to hike several thousands of miles from coast to coast in the same year (?).

I've not investigated the ADT, but I rather suspect there's a whole lot of road walking involved, indeed a lot of private property challenges, resupply challenges in a context where you don't have the usual support net of information available about that, weather challenges of various sorts. Getting water in some of the dryer states (Utah, Nevada). The amount of road walking in particular would put me off, though.

I suggest that you hike, say, the Appalachian Trail, and then study the ADT after that to see if you want to do something a lot more challenging.

Best tent to do it with (not ignoring the initial question)? I'm a fan of Lightheart Gear tents.
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Brian Lewis
http://postholer.com/brianle