The application process via Stripe will allow you to immediately start processing payments while the bank application can take up to 24 hours for approval. Both methods will require you having the card reader to start.
This is based on personal preference. Stripe covers the compliance processes for you and charges per transaction while your own merchant account has a requirement to process a certain number of transactions per month.
The total cost depends on the package chosen and the payment processor used. For example, the POS & Accounting package for 3 users cost $45 per month plus your monthly card processing fees per successful card transaction.