It's not uncommon to have a boiler reach 200-degrees (or more - remember it is under pressure like your car's radiator, so it can go above 212 without boiling when all is working properly). Most hot water boilers can't be set above 205 from what I've seen. Since you radiators were designed for steam, unless you run the boiler hot, they may not be able to give you as much heat as you want on a really cold day - depends on how it is sized. The pressure in this kind of system is low, typically in the 15-20 pounds range. Double-check the specs on the pex, and use one with an oxygen barrier if it works out. Are the radiators on a single pipe, or do they have a return line? You'll need a return line to run hot water. You might consider replacing the existing radiators with baseboard hot water units, then you could size them appropriately.
To do this right, you really need a heat load analysis, otherwise, you'll be shooting in the dark. Many older systems are really oversized. A boiler runs at its most efficient if it runs all of the time. I just had a new one put it, and it has an outdoor reset control that monitors exterior temp and adjusts the output of the boiler. It's only been in for a week or so, but it seems like it keeps the heat very even and when I look at it, the operating temp of the boiler is often in the 110-130-degree range unless it is reheating the water tank (where it goes to around 190).