Wheel/tyre size and upgrade questions

dl80
dl80 Posts: 10
edited July 2017 in Road buying advice
Hi,complete beginner here.
I got a Saracen hack a couple of months ago which comes with schwalbe g-one 38mm tyres but on checking the wheels that come with the bike, they are 622-15c.
Is this safe to use these wheels with 38mm tyres as I read the 622-17c mavic asksiums only recommend up to a 32c tyre?
Also is it worth upgrading to the mavic or something else or just sticking with what I have (if safe), max budget of £250? Would 29er wheels be ok?
Many thanks for taking the time to read