If you're afraid to lose your customer on the turn, that's one thing. I don't like the minraise particularly, but I could see an argument for just calling the turn, since you're no longer vulnerable to the straight.
However, the minraise on the river is the ugliest thing I've ever seen, and if you can learn this one principle properly, your net result will go up by quite a lot:
When the board hints at an obvious strong hand that you can beat, push.
Ok? THE ONLY SIZE OF THE BET THAT IS ALLOWED IS ALL-IN.
There's four to a straight on this board. Your opponent isn't folding any ten. However, he might not re-raise you with only a ten, so the only thing you achieve when you minraise the river is to make sure you win the minimum. He can have close to 0 hands that will call a river minraise but not a push.
The reason this particular leak gets me so riled up is because it's such a trivial leak to plug, and it's such an expensive leak to have. And pot size doesn't even factor in. I would have recommended you push this river even if the action so far had been checked around every street, and a river shove would have resulted in you betting $97 into a $5 pot.