A budget that is too low doesn't offer enough data to see what's working and what's not. Read and find out what the ideal monthly start up should be here.
A smart approach would be to work your way to the top by generating affordable leads in a short amount of time with a small amount of budget by bidding on lower position, higher quality keywords. Then start to scale.
Technically, you’ll start to see results right away; however, it takes about 90 days for a campaign to “normalize” to the point of understanding how it will perform long-term.