Garden weeds

depending on what they are, annual weeds can be killed with Roundup. Perenneal weeds with tap roots etc. should be dug out first before you put the weedkiller on.

I would always dig out weeds no weedkiller.

And if a lot lay cardboard on top to supress weeds.

Even if you spray it, you'll have to dig it out anyway, so why not just skip the spraying and start the digging. However there may be some weeds such has couch grass, which unfortunatly has to be sprayedm digging is just not effective when it comes to weeds like couch grass, if there are any traces of the plant left after digging it will grow back twice as vigourous as before.