Do you need an actual shed or could you store the few items that used to be in the old shed inside your garage/basement? You could design storage shelves/tool boxes/etc. for those needs and find those kind of projects easily within your stated abilities.
If you do decide you need a shed, you might be able to get a kit for a reasonable amount. This would allow you to stretch your woodworking skills without overwhelming yourself. My Dad, back in the 70's, bought a tin shed kit (likely from Sears, back when Sears had decent stuff) where we stored the lawn mower, snow blower, our bikes, outdoor toys, etc. With a little reinforcement, it lasted for decades. He was an electrician by trade who could do basic mechanical and plumbing work as well but not a lot of carpentry. Over the years from the time he put the shed up, he developed more woodworking skills. This allowed him to replace the tin shed with a two story "barn" which allowed him to pull up the well pump in any kind of weather which was under the shed as well as gave him more storage room.
Take the time to plan it out for current and future needs as best you can. You'll want to take into account how sturdy to make it given hurricanes come your way and how to protect from bugs and rot. Consider the pros and cons of putting it on a concrete pad versus piers.
I did a quick Google on "this old house shed plans" and they have lots of good info. This link for instance
https://www.thisoldhouse.com/how-to/how-to-build-garden-tools-shed may work to get you just enough shed to meet your needs. They claim you can make it for around $150 if you use pressure treated wood and that it'll take about 8 hours for someone with moderate skills. I find This Old House tends to explain things well but others here might have additional suggestions for where you can get good, easy-to-follow plans if you don't want to/can't afford a kit in your area.
