Mailchimp is a good mailing system.
The moment to email the client depends on the type of product, niche of business etc... So experimenting is key to success. It also depends on the content of your email, the message, the offer, the promotion, the season.
For example a, Christmas email would be suitable now, regardless of when the customer is added to the mailing list. But other emails might be bad timing.
What I do, is place myself in the shoes of the customer, when would I be ok to receive an email. And you have to be very critical of your own judgement. I consider allot of email spam. So I email my clients every couple of months, or no more than once per month.
If for example you want to request a review, you would do this between 2 weeks to a month after delivery. Not longer.
If you want to offer a promotion, maybe do it a month later.
It's all down to experimenting, I recommend reading online articles regarding the subject, read as much as possible and than create your own plan.
I hope this helps.
Interesting question, especially as it highlights one of the reasons many store owners aren't able to convert their mailing list into customers.
Focus on building a relationship with your subscribers and getting them used to hearing from you, THEN, you'll have earned the right to promote to them, and your efforts will be more effective.