I fairly recently bought a pair of Continental Road Touring Plus 700 x 37 for my Dawes Hybrid. It was previously on it's original Vittoria Raddoneur 700 x 38s which were a bit 'squishy' and didn't really handle that well. I never had a big feeling of confidence when leaning into a corner at any great angle.
So, the Contis are much better, plus whilst it's just the "one number" i.e. 37 v. 38, they're quite a bit narrower and also smoother. They also seem very tough and have a layer of stuff inside to help avoid punctures. I'm still waiting to see if they make it through the 'hawthorn hedge cutting season' though
I got them in the UK from Chain Reaction Cycles for just under £30 inc. delivery (for the pair). I just had a look on the site again and they've been reduced further to £12.99 each inc. delivery - however, the smaller sizes are more expensive for some reason (popularity?).