Some general reflections
It would be possible to do it more cheaply - by ship (Norruner) run by Smyril, again the Færoes own - from the North of Scotland - and staying in hostels. However, if you are intent upon a cheap holiday, this is hardly the place for you! Iceland is well known for its expense and people returning from Iceland to England via the Færoes reckoned that Iceland is cheaper.
The Færoes are an autonomous province of Denmark but enjoy seperate representation on the Nordic Council. It seems that a small majority is in favour of complete independence and perhaps Torshavn is destined to become the world's smallest capital.
I view the thought of starting on tips with some acute misgivings. I doubt I have the vocabulary to get over not just the extreme beauty of these islands but, more so, their difference from other places and, most of all, the great differences between the islands and villages within the Færoes.
I am still in Torshavn now and I shall wait until I get home.