Personally, I'd avoid the paintball co2 for a 60 gallon tank....I think you'd be better served getting (depending on what you can afford) either a 5 lb tank or a 20lb tank.
Why the big difference? The jump in cost from a 10 to a 20lb doesn't make the 10lb worth it imho, and the cost of swapping or refilling the tank is more or less the same as well, but with a 20lb you would have double the amount of co2, and that should last you months, if not a full year, by itself.
As far as a regulator, get a normal regulator, not a paintball regulator. Honestly, I do feel that co2 is the one part you are going to want to splurge on, as a good regulator is worth its cost. You don't want the thing failing on you and gassing your fish ever, ya know?
As far as the fish go, I actually have two of these guys as well. Mine don't do very much digging, however, I wouldn't suggest doing dwarf baby tears (HC) simply because they are a very weak rooted plant, will be high maintenance to keep looking nice, and will probably get uprooted just by the fish swimming over it as they get larger.
What I would suggest as a carpet is either hairgrass (it gets some good roots but you might want to have it in a heavier substrate that doesn't get blown around too easily), monte carlo (kinda like HC but bigger leafed and hugs the ground more, nicer plant imho) or S. repens (it will need to be cut and trimmed to keep it short, but it has amazing roots and will stay in place, its working out nicely for me although I'm not using it to cover the entire bottom as I want to try something else to carpet with as well). If you have the light for it (which you should if getting co2) hygrophilia araguaia also likes to hug the ground, and is red, which is pretty cool.
No experience with chainsword here, but I feel like it might get some nice roots.
2 things that will help you with these fish and plants...
1. Select plants that have strong root systems. Anything that has weaker roots will often find itself floating and will require re-planting. Especially carpeting plants. Most stem plants will eventually figure out how to stay down but if its a plant with fragile stems it will get very, very frustrating very very quickly.
2. Add the plants and let them grow before having the fish. However, this is not always possible but its easier for plants to do well with fish like this when they are already established. I would hate to try and get a carpet of anything small and fine if the fish are already bruising around and the plants are struggling just to adapt to the tank conditions and start growing roots to anchor down. My tank started out with large fish before I really added plants, so its been a struggle for me but I've finally gotten it (mostly) down. You might have to get creative at times.