Upgrading gutters or grading definitely helps, but another option to consider is a green roof or even just planting vegetation around the perimeter. Plants absorb and slow down rainwater runoff significantly... I've seen it work wonders without costing too much. Just something else to think about.
Green roofs and perimeter planting are definitely solid suggestions. I've recently moved into my first home and faced similar basement moisture issues. One thing I found helpful was installing rain barrels at downspouts. They capture runoff effectively, reducing water pooling around the foundation, plus you can reuse the water for gardening—pretty cost-effective overall. Combining rain barrels with your vegetation idea could create a nice, integrated solution without stretching the budget too much.
Rain barrels are a good shout—I put a couple in last spring and they've been great. But honestly, the biggest difference for me was when I added a small green roof over my porch. It absorbs so much rainwater, my basement's been bone-dry ever since...worth considering if you're handy.