Two questions up front:
Do you have any 500 or 1000 sized spinning reels that you use for open water?
Will you be hole hopping or in a shelter/shack?
If you have a couple 500-1000 size reels and wouldn’t mind re-spooling them with line (probably 3# on one and 6# on the other) that will allow you to put the full amount towards a couple nice rods. My opinion is that when ice fishing the rod is way more important than the reel.
I personally use alot of Fenwick rods, they are a great value and often overlooked.
Here is a breakdown of their ice rods
HMG Series – $30 – Moderate action
Elite Tech Ice – $40 – Fast action
Aetos Ice – $50 – Extra Fast action
They are available in numerous power ratings (UL-L-ML-M-MH …) and lengths.
I would probably go with the Elite Ice 25″ UltraLight and the 36″ Medium to start, only costs about $80 and they are really decent rods. If you want to throw a MedLight rod with a moderate action into the mix you could add in the HMG 26″ ML for $30.
Use existing reels, three rods at $110 and add some line in the mix and you could be set up for under $125.
Word of warning on the Aetos series, the reel seat is a bit funky and you may need to modify the reel “T” so it fits nicely. The HMG and EliteTech reel seats are just fine.