FIRST, let me say how disappointed I am with this forum that you have had hundreds of views and nobody responded, even with a guess! This forum looks like the wrong place to go if you need answers. I recently purchased an 06 and will be keeping the car but shopping for a new community of owners. Most car forums will supply a couple answers within 24 hours.
You can find the oil here, it's 5w-30:
http://cdn.dealereprocess.com/cdn/servicemanuals/chevrolet/2007-equinox.pdf The manual mentions GM standard GM6094M, in case you see that referenced by a potential oil brand. Any oil that hits spec should be considered fair game, in my opinion. I am not a believer that synthetic needs to go in every vehicle. ALL oil produced today is made to a spec that is acceptable to most every driver; there is no such thing as "bad oil" these days.
Also note that the recommended volume of oil for your vehicle has increased by 1/2 quart (probably because it burns oil like mine!) so be advised:
Chevrolet Workshop Manuals > Equinox FWD V6-3.4L (2007) > Engine, Cooling and Exhaust > Engine > Engine Lubrication > Engine Oil > Component Information > Technical Service Bulletins > Engine - GM dexos 1 and dexos 2(R) Oil Specifications > Page 3636
Most American manufacturers ask you to put in a proprietary blend of conventional and synthetic. They each have their own brands...Chevy is no different here. I say you would be totally fine putting in conventional, even cheapo oil. For example, you can see here that even Walmart regular 5w-30 meets GM spec:
It's finally here- updated GM4718M w/ GM6094M list | Passenger Car Motor Oil (PCMO) - Gasoline Cars/Pickups/Vans/SUVs | Bob Is The Oil Guy
I would not spring for synthetic if the manufacturer is not asking for that high of a grade, unless you take the car to the track or a place like New York City every weekend. Conventional oil run to 5-6K should do you fine. FWIW, the Chevy 3400 engine is their blue-collar workhorse that has run on countless vehicles for many years. It is not a work of art and does not warrant pampering.
Now, if this were a forum worth its salt, someone would emerge to disagree with all of this!!! Hell that's half the fun. Where are you all?