Mmmm.. you mentioned that you will be following a tour right? Wouldn't they include accommodation for you?
I really highly recommend Saariselkä for a couple of chill out, relaxed nights. The small town is a bus ride away from Ivalo Airport. Or you can grab a cab there (which is, uh, expensive...). It's uber quiet (you hardly hear anything else except the wind) and peaceful. Unless your "neighbour" is having some Finnish drinking party or something -_-;
Don't stay more than 2 nights there though... you'll seriously run out of stuff to do if you don't hike in winter or ski or go for husky rides (which can cost up to EUR100+ per pax). If you have the budget, go for the log cabins as they are definitely better for the experience. Why go all the way to Lapland to stay in a hotel? Most have a real fire place (you need to start it going yourself, of course

) which you can BBQ those sausages that you bought from the nearby supermarket for dinner while watching some DVDs that you bring over yourself.
Gotta take note though... Log cabins are pretty much
very expensive... They are usually big, for accommodation for 5-6 pax or even more.

The one I stayed before is
this. There are others that you can browse on the same site..
For Helsinki, it depends on your budget. I stayed at a friend's place when I was there, so I have no experience in staying at Helsinki's hotels. Generally, you still can find S$100+/night decent hotels in Helsinki. They are just probably a little off from the main train station.
Cost of living in Scandinavia is generally quite high... but not alarmingly high. Euros have dropped quite a fair bit, so I guess it's still manageable for us now. Taxi is expensive. Try to avoid them if you are on a tight budget. I remembered the taxi from Ivalo Airport to that log cabin which I stayed in Saariselka cost about EUR50+ per trip. -___-; Not sure if it's because it was pre-arranged or what... I only jaw-dropped when I see the meter. I'm not the one paying, but still...
Shopping... well they have H&M. I don't usually shop, so I don't know if the prices are any better there. Chocolates - Cheap, if you go after Christmas. They are pretty expensive before Christmas period...
As for food, well.... to put things in perspective, you can take a look at Rosso's
menu to see their casual restaurant prices in Finland. It's a franchise that you can find all around Finland. It's not fine dining, just casual... much like Spageddies or Pizza Hut here.
Slightly cheaper eats can be found in small eateries at shopping malls in Helsinki. I found this "Singapore Hot Wok" eatery/cafe at Kamppi when I was there in 2008, and prices are as below:
Yup, it's pretty much expensive for a plate of char kway teow and a cup of Pepsi if you compared it to the prices back home... but their portion was huge. I couldn't finish my "nasi goreng" (essentially just chinese fried rice, not really nasi goreng)...
So hopefully now you get a rough idea of what to expect when you are there...