You can save anywhere (except the situation Senza mentioned) but I have found load times are quicker if you save on the Galactic Map.
Secondary ships vary by faction, fleet composition, and personal taste. The last two are interconnected. However, some type of fighter screening ship (at least 2-3 per fleet) is a must. If you play as the IR and are using ISDs, then some type of carrier (Escort Carrier for the first 2 Eras, add MTCs for Era 3, then Venators and Acclamators for the final 2). The ISDs are tanks, so bring in some high DPS units too (I like Strike cruisers, as well as Vic-2s). Also can't forget the unsung hero of the Empire: Carrack Cruisers. For 1 Population point these guys pack a pretty decent number of Ion Cannons which can strip shields for the ISDs Turbolasers.
If you are a PA player there is the option of a similar style to the IR or the "PA special" of a Praetor anchor with fighter spam support. My usual PA fleet has a Praetor guarded by 2 IPVs, a carrier line behind the Praetor of 2 Venators and 3 Acclamators, 3 Vic-2s, and an Escort Carrier. Then I just bring in whatever else I need depending on what I'm facing.nI can take on any fleet that comes at me with this force and walk away probably only losing the IPVs.