eVar always store the values as text, even if you are passing a numeric value like "1" or "2"
Technically, since you will have to calculate the difference between the start date and end date for the search, how you capture the data is really up to you.
How do you want to report on this? How is the information being used? Will you be pulling it solely within Workspace, do you need it to be more readable? (i.e. buckets like "less than 1 week", "1 - 5 weeks", "5 - 10 weeks", etc)
Or do you need to capture the specific values? How will you account for partial weeks (3 days, 10 days, etc)... will you round these to even weeks? Round to nearest .5? (i.e. "1", "2", 3"... or "0.5", "1", "1.5", "2", etc)
Will this data need to be exported and calculated outside of Adobe... what format would be the easiest to process?
Keep in mind, that if you pass the weeks as "1", "2", 3"... or "0.5", "1", "1.5", "2", etc; you can always use classifications on this eVar to create readable buckets ("less than 1 week", "1 - 5 weeks", "5 - 10 weeks", etc).... just remember that "0" isn't valid in Adobe Classifications... 0.5 should be fine.. but 0 is not....
- 0.5 would map to "less than 1 week"
- 1, 1.5, 2, 2.5, 3, 3.5, 4. 4.5, and 5 would all map to "1 - 5 weeks"
- etc
There really is no right way to approach this, it really is a personal preference, based on how you intend to use the information.
If you are unsure, hopefully you have a Dev or QA suite that you can play with... pass values in different ways, see how the reports look, try playing with Classifications to get the "best of both worlds", try exporting the data to other sources that might use it and see how well the data works there.
