Hi there,
Like Songsam, I think three days in Siem Reap is too little.
And making the round trip to Battambang for just one night to come back and catch a flight an hour east of SR (no operational airport in Battambang) isn’t worth it either. Especially since you might not have enough water to take the boat from SR to BTB, or the last part of the trip will be by minibus instead of on the Sangker River. There’s no floating market in the area.
Spending two nights in BTB is nice, but maybe you don’t have the time (is Phnom Penh also on the agenda for this first week?).
To get to Sihanoukville and the islands from SR, there is indeed a flight, but you can also take an overnight sleeper bus to arrive early in the morning in Sihanoukville. Companies offering overnight trips: Giant Ibis, Larryta, Virak Buntham. It’s a great option when the budget is tight because it’s obviously cheaper than flying and saves you an extra night at a hotel.
For the islands, if you’re looking for peace, relaxation, and downtime, Koh Rong Sanloem is a good choice for a few days.