I would not mess with the roots on the oaks except to remove only what's necessary to get any bed border installed and the plants set in an appropriate size hole. If you do the beds right, their impact will be minimal. So basically only minimal root pruning.
The most important thing is to make sure you have nailed down exactly what light exposure you actually have, and match plants to that. West side would be afternoon sun (part sun), but with those oaks, and any trees across street, you may find you actually classify as part shade. You would also have to adjust this slightly for what zone your in. Hotter zones are going to see more drought stress than a colder zone.
The next most important thing is to nail down what type of soil you have. Many times, without prior successful beds there, you may find that there is a lot of clay dating back to construction. If that's the case, then you'll want to either build an elevated bed, or dig out a bed with a tiller, cultivator, or machine like an excavator and discard/repurpose the clay. I like to have 8-10" depth to play with if possible, but you can get away with as little as 6" if you stay with 3 gallon plants or smaller. Once the bed is dug or built, fill with good bulk garden mix from a local landscape supplier. NOT sod blend, NOT straight leaf compost (though that's not terrible), NOT anything high clay content. Best mix around my area is 35% leaf compost, 35% dirt, 15% sand and 15% processed pine. This works out well in our projects. Ask your local bulk supplier and get their recommendation. Also, initially, I like to add worm castings when installing plants as it seems to help them establish quicker and helps with drought stress. If you're really OCD, you can throw in some diatomaceous earth, but I think that's overkill if you're filling bed with good soil.
The majority of the time I see plants that aren't doing well in an area, it's the light, the soil, or both. Behind that it would be a plant outside or on the edge of it's hardiness zone. Rarely is it the oak tree beside them.