Seishun 18

My travel plan is as follows:
Day 1 - New Chitose Airport to Asahikawa
Day 2 - Asahikawa to Sounkyo to Furano to Asahikawa
Day 3 - Asahikawa to Sapporo
Day 4 - Sapporo to Otaru to Sapporo
Day 5 - Sapporo to Lake Toya to Tomakomai
Day 6 - Tomakomai to New Chitose Airport
What pass should I buy?

The following website let's you look up local train connections, so that you can check how long it would take by local trains. It also provides fares, so you can compare with the cost of regular tickets and other train passes:
http://grace.hyperdia.com/cgi-english/hyperWeb.cgi

A few of the days you wont get your moneys worth out of the pass, but it will work out well over all. good luck

www.ryanlibre.com

Am i correct that I can't use the Seishun 18 ticket from New Chitose airport to Asahikawa?

Yes. With good transfers, the trip can take as "little" as 4.5 hours. It typically requires three transfers of trains along the way.

How about flying into Asahikawa Airport instead? Would that be possible?

You can take a Rapid Airport train to Sapporo. Changing trains at Sapporo and at Iwamizawa, you can reach Asahikawa with Seishun 18, but it costs about 3 and a half or 4 hours.
Airport, Sapporo, Iwamizawa, Asahikawa;
08:34, 09:10 - 09:36, 10:21 - 10:27, 12:40 ;
11:49, 12:25 - 12:40, 13:17 - 13:30, 15:46 ;
13:49, 14:25 - 14:40, 15:17 - 15:27, 17:11 ;
15:04, 15:40 - 16:03, 16:44 - 16:57, 18:37.

If you take a Ltd. Express train from Sapporo to Asahikawa, the total required time is about 2 hours.
About 1 or 2 Ltd. Express trains are running there in one hour.
For rides on Express / Ltd. Express trains, Seishun 18 does not cover fares or charges.

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Omotenashi is right. The trip can be much shorter than my earlier mentioned 4.5 hours.

A very big thank you to all of you. My flight will be arriving in New Chitose airport at around 4pm. I've decided to take the express train to Asahikawa cos that I can rest early that evening and then start out early the next day :)