I'm down the road from you in Redcar, with a similar setup, 3.4 Zodiac and 15hp Mercury. If you want an easy launch then try the slip at Granville Terrace (near Zetland Park) in Redcar. It's where the Jet Skis launch from. But pick a very calm day.
Unfortunately it's not as simple as just buying a boat and off you go, I'd recommend RYA level 2, Tees Marine Studies Near the Transporter in Middlesbrough do a 2 day course for about £250. Also if going to sea a VHf radio (plus getting a license), plus safety equipment is also a good idea.