1. Pure sinewave is preferable, however they are not more efficient. The pure sinewave will cause fewer problems with your electrical loads though.I have just completed an extensive search for an inverter to use my other car's (Nissan Leaf) battery as backup power for the infamous California blackouts and have the following advice:
1. Stick with pure sine wave units. They are more efficient and your electronics will thank you.
2. If you are going to do a permanent installation, such as 110VAC outlets in the back of the console, you will need a compact unit that can fit in a small, well ventilated space.
a. keep at or below 300W due to cooling requirements. Consider mimicking the Subaru option. You can probably do it cheaper and better anyway.
3. For occasional use as a direct battery hookup, go big, like up to 3,000W constant power. This will run tools and appliances that have heavy starting loads. No need to be too compact here. spend money on the guts, not a fancy case.
a. consider using a 50A quick disconnect (Anderson connector) permanently wired to the battery.
2. The most important installation issue is the voltage drop along the dc cables between the battery and the inverter. Voltage drop along these cables will cause the inverter to enter low-voltage shutdown during non-insignificant current draw. As an example, if you are going to run a 300 W ac load, you're going to draw approx 30 A from the battery.
3. You're not going to put a 3,000 W inverter in a Forester (3,000 W = 300 A dc draw). A 50 A switch is not going to cut it for more than a 500 W inverter.
For a Forester or similar vehicle, you won't be doing more than charging your phone or running a laptop or similar load, and I'd recommend you have the engine running since the vehicle battery is a starting battery and not a deep-cycle battery.
Find the power draw of the loads you want to run, and then see if the dc socket in the car can supply the current (at a decent voltage). If the socket can't supply the power, you're looking at direct connection to the battery. Remember to size the wire appropriately -- calculate the dc current required, calculate the voltage drop through copper, look up the wire gauge needed to provide the needed (or less) voltage drop, and as close to the battery as possible, install your overcurrent protection, sized for the gauge of wire installed.