Landscape with weeds

I just moved to a new place and I still haven't got the chance to tend to the garden. there is a landscaped area with some flowering plants on the perimeter. On the inside of the rectangle stone area, my guess is the weeds have taken over. I need help with clearing this off and keeping this area weed-free. I am beginner and not sure where to start. My questions:
1. Should I just dig and uproot all the weeds? or should I use a spray or something to kill the weeds?
2. after de-weeding I would like to plant some flowering perennials. I welcome all the gardeners to suggest what might be a good choice of plants to plant for this year or next? I live in Minnesota.

Thanks for the suggestions.

Looks like lots of weeds in there and who knows how many seeds from them. If it were my planter, I'd cover it with black plastic to kill the weeds then dig it all out and refill with new soil. You could use a spray but I don't use sprays unless absolutely necessary. Some of them stay active in the soil for a long time and render the soil virtually unusable.

Hostas are easy care and do well in your area. I know others will have additional suggestions.

Cville's plan is excellent and I have done exactly that with great success. Black plastic is best because it keeps the light away and also cooks the weeds.
I also think a spray is overkill (nyuk nyuk) for your area.
If you are impatient, which I have been sometimes, you can dig them up. Make sure the soil is moist. Take a shovel or spade or anything with tines, and loosen, then pull the weeds up. You have to get the roots. Of course, this is more work and leaves the weed seeds and leaves the soil, which might not be the best. But as I say, if you are impatient....
Then, after you get your desired plants in, you can mulch with tree chips or bark chips or many other things (I'm sure tons of threads here have discussed the pros and cons of the various mulches).
How much sun does your area get? How much rain? What is your climate zone? Hostas sound like a great idea, and we can come up with more ideas if we know what your area is like.

I have another suggestion. I think your stone-enclosed rectangle is perfect for weed-flaming! I have a mini-Dragon Weed flamer, that uses the little Coleman Fuel propane tanks used for camp stoves and lanterns. The miniDragon costs about $40, I have had mine about 15 years.
To torch weeds: it works best when they are less than about 3" tall, so you would want to just pull or quickly mow the big stuff first. That should take about 10 minutes. Then you flame the short stuff. Then you go over it about every week for a month or so, until the weed seeds already there have all sprouted and been killed. By then it is fall, which is a perfect time for planting. Put down mulch after you have put in your new plants, to keep new weeds from sprouting. Preen is a brand of weed preventer granules you can also use. You can buy it at Lowes and just sprinkle it around. It prevents seeds from sprouting.
Weed-flaming is nice because there is no toxic residue left behind, and it does not disturb the soil which brings up old weed seeds that are just lurking, waiting for a bit of light to trigger germination. And now you can weed standing up, with a cool drink in your other hand!
But- of course there is fire risk-do not aim it at bark mulch, or dry grass, or your house, or a wood planter.... and I always have the hose right there if I goof. And don't let your 15 year old son see it because he will love the idea of setting things on fire. In fact I usually do this in rainy weather. It is great for gravel paths, and weeds sprouting between bricks etc.
have fun!

The more you dig, more weed seeds will be exposed to light and consequently germinate. I don't think you need to go as far as replacing all of the soil though. Torch (Bernzomatic is another brand), pull or cut to the ground as many weeds as you can. Covering with plastic to kill weed seeds is a good idea but it's getting a little late in the growing season to do that effectively - you need several months of heat build-up in the soil (solarization) to kill the weed seeds. I think if you put down a heavy layer of leaf mulch (any old leaf piles on the property?), it should keep the existing seeds from germinating and improve the soil gradually. If you want to plant perennials in the fall (good time and good prices), just pull the mulch away from the area enough to plop the plant into the ground.

That hasn't worked for me, but maybe it will for someone else.