Can't really help with an exact set of suggestions. I can say that if you have a set budget. And $600 these days wont get you much. One thing I can say is check out Dell Refurbished.
I've suggested and even configured, ordered a few for friends who were a bit iffy in deciding what they needed and wanted.
Refurbished doesn't mean that they came back defective and were repaired. Companies and organizations who order quantities of the same computers often cancel or modify their requirements.
Dell builds usually on demand. Their direct refurbished line will be brand new, unused. Perhaps not exactly the "today" specifications of the latest-greatest. And you can get a nice pc for quite a bit less with full warranty.
Just a suggestion.
"I use the laptop to mainly surf the web and keep up with my finances, money and bills. I would like to have at least a 15" screen and having a touchscreen is a plus".
As far as Asus, HP goes. And others you may consider. I'd think $600 (new) would get you a laptop. A quality, long lasting one? Not so sure. Now. If you could get a $1000 lappy for $600. Good deal, don't you think?
Surf the web doesn't need a killer Nvidia graphics chip. Nor a pinnacle, top of the line Intel, AMD processor.
12-16 gigs of memory will get you by just fine.
I'm personally an Asus fan. Brands aside. The one thing is the batteries. We discussed that here someplace else.
I repair these critters. Batteries. Cheap laptops have cheap batteries. Asus suggests that you don't keep the charger plugged in all of the time to make them last. Like you see on phones where 85% vs full charge is suggested to preserve battery life.