Due to you looking to dive in, I'm thinking of budget friendly software.
Fusion360 has a free user option with limitations compared to their paid for licenses. Personally it's still great for a hobbyist.
Blender is another free option as Biskt has mentioned.
Solidworks released a Hobbyist option for $15USD/month or $48USD/Year, I enjoyed Solidworks in my time during high school.
Tinkercad is also a browser based free choice, this I've seen many use for simple projects.
Hope this helps! I personally have only used Fusion and Solidworks, both have treated me well. Blender I've always had a tough time starting out with, it just seemed a little much at first. But that's just me.