The Putnam Branch would do no good for rail transit in the NYC area, as it would dilute service on the Harlem and Hudson. Better to improve parking, track, power systems, eliminate crossings, etc, on those two lines than to have a third parallel line to dilute service. Branches are also problematic in terms of diluting service, versus improving the main line service and beefing up infrastructure and trains.
In terms of priorities, there are a ton of people today on all three lines driving to stations further from their houses because there isn't enough parking. I'd deal with the parking and station facilities on existing lines first and I think there may be some modest ridership to be gained on the existing lines. I'd also look at TOD and zoning, which could further increase ridership over time without increasing parking facilities. Moving from open lots to garages wherever possible could also both free up land for TOD and drastically increase the amount of available parking. I'd also make all parking free on weekends, and make better provisions for longer-term parking for people traveling elsewhere via rail or air.
There may well be reason to go north of Wassaic, but I'm not sure what the connection at Chatham would gain anyone. A connection to the Lake Shore Limited would be mostly redundant to connections via Albany. If anything, I'd go to Millerton and end there, as that provides a nearby connection to parts of Connecticut as well, so there might be some critical mass of ridership. However, I'd improve the upper Harlem service with more sidings, and higher frequency service with DMUs first. Electrifying to Danbury and Poughkeepsie, combined with more frequent DMU service on the upper Harlem that required a transfer at Southeast would finally get rid of the pesky dual-mode locomotives.
The Poughkeepsie Bridge is too far north. The connection that needs to be made is a new railroad from Suffern across the Mario Cuomo with a connection at White Plains to shoot down an improved Harlem, and finally a connection to the New Haven at Port Chester to go to Stamford. That's all new trackage, and would have to follow the highway, so it would be astronomically expensive, but also necessary for growth and regional connectivity.
The former Erie Main would be very useful for Metro-North West of Hudson, in combination with the cross-Westchester service to White Plains.
In fact, the only Metro-North track I would re-activate would be the Harlem up to Millerton and the Erie Main, everything else would be brand new railroad (Suffern to Port Chester with NYC 3rd rail from Suffern to White Plains and 12.5kV60 to Port Chester), using existing rail routes that don't have passenger service today (Danbury to New Milford), electrification (25kV60 from Highbridge to Albany and down the West Side Connection to a phase break with Amtrak's 11kV25 system, from SoNo to New Milford, and Shore Line Junction to Springfield), or local improvements to stations or new stations (Barnum-Bridgeport, Devon Transfer, Orange, etc).