Using the inbuilt tools:

To see your total product count, go to your 'all products' page, and add /count.json onto the end. The entire url should look like this:

https://[YOUR-STORE-NAME].myshopify.com/products/count.json

See how many products in a collection:

https://[YOUR-STORE-NAME].myshopify.com/collections/[COLLECTION-ID].json

Total customer count:

https://[YOUR-STORE-NAME].myshopify.com/customers/count.json