What is the best mode of transportation to the islands - air or sea?
Have you looked at how long that ferry/cargo boat is? I enjoy a ferry trip as much as anyone, but it's hard for me to imagine any scenario where taking that boat makes sense. Be sure to account for the number of days you would need to spend on that boat. Might be a rough crossing, too: lots of big, open ocean to cross, and there are storms all year round. You'll get plenty of chances to hop inter-island ferries while you're there. We flew in and out from Edinburgh and it was great. I'd do it again the same way.
While there, is it best to rent a car?
Yes! I'd say it's quite critical to have a car. There is an extensive (and interesting) public transit network, but like in many places it's designed for locals, not tourists, and having to rely on public transit will very much limit your options and extend the time required to do/go anyplace. Of course, if you have infinite time, you can manage to reach many places by public transit, but the Faroes are exactly the kind of place where you get the greatest benefit from having a car. I've heard from many people who were dedicated to the idea of public transit, but who did not have a great experience in the Faroes. Cars are not cheap (but nothing is there, everything's expensive). Reserve your car far in advance for the best/least expensive options. Roads are great, driving is easy (well, the single-lane, two-way-traffic tunnels are a bit, um, interesting, and require nerves of steel, but you get used to them).
There are lots of tunnels, some old, narrow and rough (look like they were hacked out of the mountains by an army of dwarfs with pickaxes), others are modern, wide, smooth and have cool lighting); some are short some are impressively long. They're still building several long ones.
Any recommendation concerning lodging?
Lodging is in very short supply, so it's expensive, and often at least a little bit funky (sometimes more than a little). Reserve well in advance to avoid being stuck in some canvas tent or a bunk in an old school bus, miles from nowhere and paying a fortune for it. Have a sense of adventure and low expectations. There is a new, chain-style international hotel (was being built when I was there, can't comment on it other than it's one more way the place is rapidly changing).
Understand what you are getting yourself into. It's a long, long way from everywhere. Prices are high for pretty much everything. Most importantly: while it is ruggedly beautiful and very scenic - especially when the sun comes out - the weather is often "challenging." We were there for a week. When we arrived, the sky was clear and blue, and everything looks shined and spectacular. We had about 2 days like that, then the clouds rolled in. For the rest of our time there, it was mostly rainy, windy, foggy, cold, claggy, and moist. Visibility shrank to nearly zero, so while the scenery was gorgeous, you couldn't see much beyond spitting distance. This was in July, midsummer, statistically the "best" weather of the year.
There are no real major indoor attractions (museums, cultural treats) so on very rainy days (and we had a lot of them), your choices are to sit in your room, or go out in very rainy weather (I live in Seattle, a little rain doesn't deter me), but we had a lot of zero-visibility, low clouds and very foggy, days, plus hard driving rain. Some people get lucky and enjoy many sunny days there, but I would not count on being that lucky. My advice is to ask yourself how many usable days you need to see the place, then double or triple that number, because half or more of the days you are there may be very wet and stormy. I loved it there, but when we flew back to Edinburgh, I was happy to find the sun was shining there.
Have fun!
