There's a lot of subjective calls to be made to your request for a "go-to" answer here. If you get 50 responses to your question, it's very likely that you'll get 50 different answers. So take mine with a grain of salt and mark this one up as nothing more than #2. Following is how I do my logo work.
1) Figure out how the logo will be used. It looks like you've made some inroads here, which is good. But are you sure that website/stationery/business cards will be the only uses? Could it be used for signage? For small trinkets like pens? You really want to consider every likely usage for the logo you create.
2) Make it easy for yourself and design big. Because I try to be incredibly lazy/efficient, I work with the Illustrator default page size of letter for US measures or A4 for European sizes. And since my logos tend to be more wide than tall, I set the page for landscape and then go to work. Working large makes it easy to arrange type/elements exactly the way you want them.
3) Go to town and experiment with the logo design to your heart's content. But keep yourself honest and be sure to test your work by printing it at the smallest size you're going to use it. That may turn out to be business card-sized, because the card probably won't be completely filled with the logo — as a general rule, figure proportions of about 3/4- to 1-inch wide for your business card layout. Of course, if you're working with something smaller like putting it on pens or using it as small art on the website, use that even smaller size instead. If it doesn't print cleanly at that smaller size, simplify your design(s) and try again as needed until you can clearly identify the look you want at the smallest sizes your friend/client will be using.
3a) Pitfalls — there are two things you'll want to be very careful about when designing for both print and web reproduction:
- Line Width/Detail – Since you're designing large to make things easy on yourself, elements which look small in the large layout, thin lines and tight curves which work fine while you're designing may look pretty poor when you reproduce them at small sizes. Especially on the web, where diagonal/curved elements aren't defined cleanly onscreen. One way to fix that is to refine the design of your logo to avoid those problems. The other way is to specify a minimum acceptable size for pixel reproduction and stick to it. Depending on the situation, either option may be the right one for you.
- Color Choice – I'm inferring from your question, rightly or wrongly, that you are a web-centric designer. There's nothing wrong with that. But when designing for both online and print reproduction, color choice can vary widely between onscreen and print. Color choices that are easy to see online like bright greens, warm reds and light browns are just impossible to match in CMYK print reproduction. Similarly, rich colors which look luxurious in print can be far away from web-safe colors and look dithered/mottled onscreen. Especially at smaller sizes online. So while I live by my black-and-white laser printer in my studio, I'll pop for color proofs run at my nearby Office Depot for logo work for two reasons: one to review my color choices and two to see how they reproduce in just about the most indifferent color printing I can find.
4) Create my output formats. I keep the native Illustrator (.ai) file, with all font information and un-rendered graphics, so I can make changes/updates as needed through the review process and my friend/client does not.
You'll see a lot of comments from other responses after mine about my next choice, but for print reproduction I give clients Encapsulated PostScript (.eps) files to share with print vendors. I convert all font information to outlines (effectively drawings of the letters) and expand all effects I create for graphic elements, which don't blow up for simplicity's sake and to reduce the chance of someone editing the file and messing it up. I place them in Acrobat PDF files for the client to review/proof, and tell my clients to just give the logo files to print vendors to reproduce. Some folks will tell you this choice is primitive/archaic, but it's still the universal format which even mom-and-pop small-time vendors can reproduce easily.
For web, I create .png and either .gif (for simple flat logos) or .jpg (for complex gradient/transparency-laden logos) files for onscreen use, depending on which result looks better for the end product.
So in short, I keep one file format only for me (.ai), and three formats for thee (.eps, .png and [.gif or .jpg]) to cover client needs.
Don't let others discourage you. It takes guts for an experienced veteran graphic designer to admit this, but one of the dirty secrets of this business is every single one of us has learned what we know today on the backs of what we've previously done for our clients. Mistakes happen. If you make one, you'll fix it and make it better for them. And truth be told, there's very little you can do to a type-centric logo design which cannot be fixed.
Good luck. And have fun doing this job for your friend. Don't forget to read all the responses you get to your question and take them to heart. Try all the ones which make sense to experiment with, then throw away the ones which don't work for you.
Hope this helps,
Randy