You need to look at any plan documents for benefits as they will help you determine eligibility for things like 401k, health insurance, etc. Some of the determination is based on federal/state law and other choices could be employer policy (while keeping to the laws)
For timeoff, you need to look at state and local laws to see if there are any mandatory benefits (such as if you were in San Fran, CA, there is paid sick time for certain situations). I think Hawaii also has some type of mandatory benefits. What state are you in?
For PPACA (Obamacare) and health coverage in the future, there is a calculation that will be used based on their average hours over a certain time period and whether the employer is "large" or "small".
Past that, employers generally have the right to decide the parameters for eligibility and accrual of benefits. Our employees have to be classified as "full-time" to receive any paid time-off. It is a specific status, not just about the # of hours. We watch hours pretty closely and have very few employees that go back and forth across our definition. If you have a lot, then I would suggest accruing by the # of hours worked, so they benefit based on # of hours worked. You could even tier it so they earn a higher accrual in a week that they work full time and less in the weeks they work parttime (if you want to reward full time). You possibly could set a minimum that can be used (like 1/2 day or 1 full day)...again here you would need to check state laws. One last choice you might have is whether any accruals will be paid at termination (that is state specific).