OK, when you say 'press fittings", I have to presume you mean something like Victaulic's VicPress- a fitting which is crimped on the OD of the pipe, where the liquid seal of the fitting pressed collar and the OD of the pipe.
Those systems require very good surface finish on the OD of the pipe to work reliably. Vic Press works only with stainless sch10S pipe. I would have zero confidence of such a system remaining leak free long term on the OD of galvanized pipe.
Conventional roll- or cut-grooved Victaulic can and does work reliably- it is widely used for hydronic and potable water and sprinkler applications. At 1" though, all those applications would tend to use threaded pipe- grooving starts to become popular at sizes 2" and above at which point threading becomes impractical.
Welded pipe for a water service is overkill in my opinion, but that depends on where the pipe will be located, the consequences of a leak and the opportunity and access for repair. It also depends on the external and internal corrosion conditions: threaded galvanized pipe has the advantage of corrosion resistance on both the OD and ID without further processing, whereas welded CS pipe will need to be painted on the OD (a very labourious process for 1" pipe!) and will have limited corrosion resistance on the ID. That of course doesn't matter much if it's closed- loop water which does not have fresh water added to it routinely- no oxygen and no food for microorganisms means no meaningful corrosion in closed loop water systems.
All this discussion also depends on pressure and temperature: we're presuming this is "water used for heating", i.e. hydronic heating water, not water above its boiling point!
