Set a high CPC so that your ad appears in the top 3 positions. Keep changing your ad copies till you get a good CTR. Once you get a good CTR, it will start influencing your ad position. Once that happens, reduce the maximum CPC.
A low daily budget is a bad idea except for times when you have brief periods of indecision. If your ROI is poor, then turning the budget down just ensures that you lose money slowly rather than quickly.
In most cases, the best option of the two you mentioned is to crank up the budget and turn down the bids.
But this is not all about bidding strategy. There are many other factors that determine whether your campaign is successful.
It is very hard to fail with a low daily budget. It's also nearly impossible to succeed. If you feel that you're fence-sitting with your campaign, it may be time for a reality check.