I read several threads here concerning indoor lighting for plants, but the language/terms used are beyond my ability to understand.

Bottom line: I'm a novice, looking for the best lights to grow seedlings indoors for my vegetable garden. I plant to use a Home Depot adjustable shelves, but I have no idea what type of light fixtures and bulbs to purchase.

Should I go with LED or HID lighting? And specifically, what should I buy?

Temery, here's a recent topic related to your question. A lot depends on how deep your pockets. My personal opinion is don't spend a lot of money until you get some hands-on time. Here's the link to the topic.:
The thread "Best (inexpensive) lighting options for indoor plants?" in Ask a Question forum

I just read that LED lights are not recommended for seedlings because they don't give off any heat. So unless you have the plants in a very warm room the seedlings would benefit from the above heat from regular florescent tubes and a cheap shop light. Beneficial to both the seedlings and your pocketbook!

You might want to go back to your profile and add your zone and state so if you have any more questions we're better informed to help you.