I'm going to keep this away from being an opinion piece as those are off topic for this SE. So lets just look at some things to consider:
- New parts will be more expensive, even from Rock Auto, because remember they have Rock auto too, they just tack on to that price when they sell it to you.
- Used parts may need repair of their own, especially since it sounds like they are hard to come by, so you may not get used ones in the condition you need.
- If you take the time to hunt through the various junk yard web sites to find what you need, it takes your time, and then you need to either go pick up the part, or pay to have it shipped. All of which is time consuming and potentially costly.
- If you order new, it's a couple of clicks and the parts go to him directly.
How quickly do you need the car back?
- If it's very fast, pay the money and don't look back. Anything else will draw out the process. Potentially a lot.
Will the shop even go that route?
- Some shops will not work with the parts you bring in. You'll have to work this out with the shop directly. Many shops will only do it if they increase the labor rate. Most shops are not making a ton of money, but the income comes from both parts markup and labor. If you bring the parts it may not even be worth it for them to do the job.
How much would you really be saving anyway?
- If you look at the estimate they gave you, it's broken down into parts and labor. If for whatever reason your repair is 80% labor and 20% parts, your not saving enough for it to matter. Where your pain point is on this is entirely up to you.
What parts do you actually need?
- The last part of your question about what general parts groups do you need is entirely dependent on the particular make, model, and year of your car. To be honest, if you're asking the question, you might want to let the shop handle it. Unless of course they are willing to let you hunt for parts for them, in which case get a detailed list of the parts that are needed. Then you can search for them on the web.
I think those are the major considerations. The decisions are all yours to make. Sadly your question was about which is "better". But only you can define what better means. You can optimize for money, time, and quality of the work. But you can really only pick two of those.
Do a search for used auto parts on the web. I think you will be surprised by how much is available, and sadly how high the cost can be after shipping.
I hope that gives you enough information to at least go forward and do more research both on the web and with your repair shop. Search for parts on the web, and see what the shop is willing to do to help you bring the cost down. Whether that's let you hunt for parts, or some other potential money saver. To them it's about labor and parts. Work with them to see how you can bring the price down but still make it worth it for them to do the work.