Hi there, JMB!
Ana here, from the Shopify support team. :)
You can create 301 redirects manually within your Shopify admin, in Online Store>Navigation:
Here's some documentation with the full steps involved in doing this: https://help.shopify.com/manual/migrating-to-shopify/url-redirect
Hope this helps! :)
How many pages are on your current store?
From an SEO point of view, get this wrong and it could ruin any organic traffic you get so it is imperative to get right.
If you have an existing store, the first step is to crawl it and see how many pages you have there to redirect. Do you have an idea of how many products and category pages you have? Do you have an integrated blog?
If you want some help then please feel free to email me timsilver1980(at)gmail.com
Hi JMB, we can assist if you still need a hand. As pointed out on the forum this can be done manually in Shopify, using an app, or using the Shopify API and scripting (we have done all of these). Also, there are utilities that can help you extract old URL's and map them, and/or you can use your old sites database to secure the old URL's.
Let us know if you want some help: email@example.com