I don't want to sound like a dick to anyone (honestly guys, no offense intended at all) but you shouldn't listen to people that don't work in the field of design and follow industry recognized business practices.
That being said
First thing to remember is that you are LICENSING YOUR artwork. Let me stress that it's YOUR artwork and that they are licensing it separately. If they are hiring you, it's because they trust YOUR judgement to do work for them. And, they are not purchasing your art, they are LICENSING it - meaning that you give them license to use it the way you and them mutually agree upon and work out in a legally binding contract, or better yet, series of contracts.
Here's the process -
1. Determine what they need. Talk to them extensively and prepare a document that outlines what they need in a subjective way - meaning what they want the project to "look and feel" like. Write all that up based on what they tell you and what you interpret from that. That's called a "Project Brief". The point of this is to make sure that if halfway through the project they change their minds, or they say "That's not what I said I wanted" you can say "Well, according to this document you put your sig on, that's EXACTLY what you wanted"
2. Determine exactly what they want you to deliver to them. Is it a graphic? Or, a PSD live file with all the layers they can mess with? Or, a graphic and the rights to use a logo treatment on a tshirt you created for the graphic? Put this all in a document, this is called a "Work Order". This is what each person is to expect of the project objectively.
3. Determine how much work you are willing to do, what you are going to allow them to do with the work, and how long you want them to use it for etc.... and how much you're going to charge. Put this in a document, this is called the "Licensing Agreement".
For the sake of licensing, generally you will send them a flat, print ready PDF. They aren't allowed to make changes without asking you, and you reserve the right to make the changes for them (to be charged hourly, of course).
If they want to pay you more (generally a lot more) they can purchase more rights, or all rights (essentially, they own the art, it no longer does and never did belong to you legally).
I believe that bad business ethics and not doing things right de-values the industry as a whole. Some people think it's ok to do work for cheap because it's building your portfolio. In some cases, it's ok to do work for cheap or free. But, in most cases, doing work for cheap just leads the client to assume they are going to be getting work for cheap from you. Your job is to educate them why creative work is worth something.
If you need examples of any of those forms, I'll email them to you. Just let me know.
Sooo, in short, if you have a personal relationship with the company and you feel comfortable sending them live files, do so. But it sounds like you dont - so don't. Explain to them that you want to maintain the integrity of your art (and that it's YOUR art), and so long as you are well spoken, hopefully they will understand.
