Renting camping equipment is pretty difficult and might be expensive because camping is not so common in Japan.
I have been in Hokkaido around this time 2008, your price seem pretty high but that depends what you want. Im gonna list what i paid in these places
A note to start this: I could speak a fair bit of japanese so it was always easier for me, but don´t be scared if you just speak english, local people on the smaller villages will go out of their way to help you! Most placed i stayed during my hokkaido trip where so called minshukus (private homes renting out rooms) or ryokans. I usually found the cheapest ones on arrival asking at the tourist information,
Furano: On arrival i asked the local office if there are any cheap minshukus and was directed to one that cost me 5000 yen for a room with dinner and breakfast (you usually pay by room, so this would be 5000yen for both of you + extra fee for 1 person dinner and breakfast, guess around 1500-2000yen). I do not remember the name of this place, but im sure people will be helpfull if you as the tourist office next to the station.
Be sure to say that japanese style is ok and that you don´t need a western style hotel as this are more expensive! I think that place i stayed would be ok for a couple as well.
(japanese style just means you will sleep on the floor on a futon wich is quite comfortable)
I do not know about your night 2/3 but i think you should splurge once and an onsen town is always a good place to be!
Wakkanai: I did the same thing as in Furano, uppon arrival i asked someone in the station and there is a nice small place right next to the station (go out and turn right). The lady at this place was so cute and nice, i´d definetly recommend it! She doesn´t really speak english, but im sure you´ll be alright. I paid 3500yen for a small room, i guess you´ll have to pay a bit more but should stay under 5000yen. Its really right next to the tracks, but don´t worry about noise as there are only 2-3 trains a day and none at night.
this is a picture of the place in wakkanai. Its the building on the right with the blue writing saying Ryokan saihate
Rebun:
I hope you are going to rebun for hiking because it is very beautifull.
Rebun became one of my facourite destinations in Japan because of the magical, crazy place i stayed. There is a youthhostel at the bottom end of the iland called momoiwaso (momo = peach, Iwa = rock, so = in). It is very close to the,... you guessed it: peach rock and to the catrock. It is one of the crazy places you have to visit when you are on rebun (crazy in a good way). Hm, where should i start: I guess it is more fun if you speak a bit of japanese but they welcome foreigners who just speak english as well (there were 2 when i was there. Sleeping is in dorm rooms and men and women are seperated (as far as i know). Price is 3050yen and you should book ahead than you can book dinner as well. So far to the "downsides"
If you book ahead you will be picked up from the ferry wich is the first crazy thing. They will wait for you with momoiwaso flags and scream Okaerie (wich means welcome home) even if you are there the first time. You can answer this with "tadaima" (i´m home). They will then put you in a truck and drive you to the youthhostel. While driving you will go through a tunnel wich is the "momoiwaso time tunnel". In Momoiwaso the time is 30min different from the rest of japan ( not really but they take it serious). After they drop you off you will be welcomed again by any noisy instrument they just could find and you have to say tadaima again. Then you check in and enjoy the scenery or do some smaller hikes. In the evening is a meeting with different characters talking about the hike and rebun. The next morning early the bus will leave and drive you to the top of the iland to start the hike. The hike takes all day but you can cut it short by taking the bus after 4 hours. This was one of the most beautifull hikes in Japan.
When you come back in the evening they will welcome you home again.
The place is also directly by the sea and in the sunset you can see the cat rock. They also have a special sond they will only play if you can see the sunset (if its not cloudy).
When you leave the iland they will bring you to the ferry and sing you and the other traveles a goodbye song.
So if you get the chance, stay 2 nights at this magical place and do the hike. I have posted 2 times on my blog about this and also it is in german, please have a look at the pictures
post 1 post 2
I recommend to get someone to reserve the night on Rebun so they know you will be comming and you can eventually order food (there are no restaurant around). Also the bath in this place is a japanese style bath where there is 1 room with many showers and a bath tube. Shower first and than sit in the tub if you´d like (showers are to sit down). Men and women are sepperated.
I promise you you will have a good time at this place!
If you have more questions let me know. If you want i can look up the phone number for this place and eventually for 1 in Furano.
Please enjoy beautifull hokkaido!
Edit: the best onsen i stayed was in Tohoku just 1 hour south of Aomori. So if you trek through there you might wanna spent a night there.