The money for putting shows together, and submitting to juried competitions and grants can be difficult. I've spent several thousand dollars getting 25 framed prints together. Initially, I had a show scheduled at a local public gallery in my town's library. I had a year, and it gave me impetus to figure out just how I wanted to print and frame the body of work I was doing. So, I paid for prints frames a few at a time every two or so months until I had it all ready. The upside, now it's ready to go, and I've managed four solo shows this year.
I think it's important NOT to change your style or interests to meet a grant's requirements. It can prove to be a distraction, as you say, Janet. Find grant opportunities that allow you to pursue your work... not their agenda.
Pick juried shows that are regional... you don't want to add a boatload of shipping. Portfolio reviews may be more bang for the buck.
I think just careful, focused submissions for grants, juried shows, and portfolio reviews are the best bets. Read the submission requirements carefully, and be sure it's a good fit for your work and budget.