Well, you jumped into a nest of Partner people. Many of us use or install Avaya Partner systems, and are (mostly) happy with them.
Avaya specifically markets the Partner to upscale residential use; a simple control unit handles three phone lines and 8 phones, and can be grown to much larger capacity. Voice mail is an easy / inexpensive option, and most other features are built it. A multi-line cordless handset option is available, though expensive.
One particular plus to Partner is that you can plug in regular phones and accessories to any port. So, if your kid absolutely loves their M&M phone, they can still use it.
Personally, I am very pleased with my Partner system for residential use. We have about a dozen stations, 3 lines, voice mail. We use the "Euro" 18 button sets with lighted display and they work well.
Your first order of business is to get the wiring in the walls done correctly. Proper wiring will support nearly any phone system. Typical residential phone wiring is junk, and will cause you many headaches.
Every place you want a phone, you need a wire run back to a central location. (Garage? utility closet?) This is called Home Run Wiring. Such wires are useful for phones and for networking connections. So-called CAT-5E wiring is inexpensive, yet supports high-speed network connections, and can be used for phones. (Consider running 2 wires to each location). Obviously, you need to know more, and also think about video/cable/satellite wiring, etc.
Some developers offer advanced "structured" wiring, using thick cables that contain CAT-5E, telephone, and other wires, all strung back to a cabinet. Nearly every installation I've seen has run the wires back to a bedroom closet, which seems inconvenient to me.
Partner systems have been made for nearly 15 years, and there's a good market for used and refurbished parts if you want to start cheaply. To get the latest features, you want the Partner ACS model, but earlier types (Plus, II) are very good. All the phones are interchangeable between old and new systems; the newer phones ("euro style"

are more reliable and have larger displays, more buttons.
Another option to conisder is the older, smaller Merlin systems, such as Merlin Plus. These are very inexpensive on the used market, and used some classic phones that some consider very attractive. Smaller Merlin systems didn't have Caller ID support, however, and voice mail integration was not as clean. Yet there are literally millions of Merlin systems out there.
Some people are now forgoing wired phones and getting the Panasonic (or other brand) multi-handset cordless systems. While not of "business quality", they offer a lot of bang-for-the-buck. No wiring needed. Support for up to 4 lines, 8 handsets. Intercom between handsets. Every handset gets a charger. Built in voice mail, directory dialing, etc. Worth checking out if you like cordless phones.