I'm Miles from the Social Care team at Shopify. You'll be happy to know you're able to set up shipping without needing to reply on price or weight - though you will need to select one in order to set up the shipping. I'll explain below.
Flat shipping rates charge a specific amount for shipping at checkout. You can create flat shipping rates for any order within a shipping zone, or only for orders whose weight or price is within a certain range. For example, in a shipping zone for Europe, you could set a flat rate of $10, and another flat rate of $5 for orders that are over $50.
In your case, let's say you'd like to charge $5.00 for standard shipping and $10.00 for express. To set this up, you'd add in a rate with no conditions and just label the 2 rates as Standard and Express.
Once you're done, it should look something like this:
For more information, check out our help guide on Setting up and managing your shipping and delivery.
If you have any questions, please let me know!