The new style hook up is a Marshall Type large Acme nut which can be tightened by hand. New style tanks have an internal check valve which prevents gas flow until a leak tight connection is made. Adapters are available to convert the old style POL fitting to a new style Acme nut but the cost is almost the same as buying a new 20 lb tank. If you have previously visited the US and have an older style tank you should be aware that the filling station will require you to change the valve on your tank for a new style before they will fill the tank. A new tank is almost certainly the cheaper alternative.
Tanks are available in hardware, camping stores, and at some filling stations.
Larger tanks are not generally available. Some European manufacturers of propane tanks recognize that it is inevitable that you may wish to try and fill them abroad. They may provide adapters for use in different countries. Ensure you are offered the newer style US adapter and not the old style. You will still have to persuade the US filling station to use the adapter - depending on the operator's approach, this may be problematic.