Figured this could be helpful to future first-time travelers to Lima, as I have found various conflicting information on the web.
Please note that this only covers LIMA, as I am not visiting other parts of Peru.

Arrival into LIM Chavez airport

• Arrival and immigration is fairly straightforward here. There is a separate line for ABTC/APEC folks as well, though I didn't need to use it. There were no immigration or customs forms to fill out IF you have nothing to declare. Basic questions are asked about your trip, as well as arrival info (flight #) and stay duration. Passport was NOT stamped (this is normal; I asked the agent). Your picture will be taken.
• In the baggage claim area, there seems to be only one kind of ATM, geared toward tourists and not affiliated with a major bank. There is also a money exchange office but I was hoping to avoid those.
• After you pass through customs, there is a mini area with car rental and a few taxi agencies (including Taxi Green). After you exit the mini area into the arrivals hall, this is where the "taxi? you want taxi?" crowd is. If you arranged a car pickup, this is also where your driver is likely going to be (holding a sign).
• I walked around the arrivals area looking for a major bank ATM - no such luck in the immediate area. There was another one of those tourist ATMs and a money changer, so I gave in and exchanged $100 USD for soles. The rate was 3.52 (vs 3.65 official) with a 3% commission, which meant I lost about 6% in the transaction.
• Found my driver holding a sign with my name and he drove me to my hotel in Miraflores.