I can recommend GMPartsShop.com for this thread based on my recent comparison shopping and all of one order placed last Tuesday. They said it would be delivered by Friday unless I heard otherwise and everything (7 parts) did arrive that day by 10:00am. They don't stock any Aveo parts on site, so it's ~2 days from Chevy plus time for the requested shipping service. They appear to be a Web-sales arm of an AZ based dealership, so a key person leaves or they get busy and YMMV.
I poked around on five of the higher profile GM parts sites over two days waiting to hear back on a order attempted at my first vendor choice; otherwise I never would have spent time for this sort of comparison. The following considerations are a snapshot of why I went with GMPartShops as the alternative, but are fairly generic to evaluating any on-line parts supplier. I'm sure others would be better for different baskets of parts or circumstances, so it pays to shop around.
Here's what I found to be good:
Total cost: Second lowest price of five vendors checked, no handling fee, and comparable shipping.
Flexible minimum quantity: The basket included a few small bits that others upped to minimum package quantity. I was surprised they would actually send a single window crank snap ring (to replace one shot onto the lawn). Said they can't do this in all cases, but at least try where Chevy already has open stock. They appear to get quick and accurate confirmation on availability from the warehouse.
Check for discontinued parts: Some sites are configured to block orders for parts that have been tagged as discontinued by GM even though they may still be available in the regional inventory. These guys don't currently do that, so was able to get one of the discontinued 2004 right side mirror covers that could not even be ordered on some other sites.
Paypal accepted: A personal payment preference not offered yet by many others.
Good communications: Pre-sale phone support is offered - likely an answering machine, but were good about returning calls within a business day. Robo-emails for confirmation and status changes were prompt and fairly meaningful.
The one disadvantage was that they didn't offer a two-day shipping option. However, their overnight service was only about $5 more than two-day service at most other vendors.