The problem with putting LR in a hospital tank isn't that the bacteria will die, some will but a lot will still live, is that the LR is going to absorb some of the copper. This will cause you to have to add more copper to get it up to the correct level. Also, if you plan on using copper you need to get a good test kit, because if you don't treat at the copper level it's not going to work, and if you treat at too high of a level the fish can actually die. I use Copper Powder, as it lets you treat higher level without the worry of over dosing.
If you're sure that your fish have Ich, then it's probably better to use Hypo. If you go that way you're going to need to get a Refactormeter, as measuring the SG is very important.
As for a tank, it's probably best to get a large Rubbermaid container, like the 50gal. The good thing about the Rubbermaid containers is when you're not using it to treat fish, or quarantine them, you can use it to store things.
Also, there is no magic cure to ich, it takes time, usually 2 weeks after the last spot you see fall off the fish. And you want to leave the main tank empty of fish for 6 - 8 weeks, this way you'll be sure the ich in the main tank is gone. Going forward you want to make sure you quarantine all you fish, even if you get them from places that say they've quarantine them.