2x15miles is a long commute and you will need a bike that is efficient, comfortable and practical.
I would look for a road-style or touring bike, but one with more tyre clearance, to accept 28mm tyres + fenders. Check availability locally of old style 27" wheel tyres and inner tubes; 700c is the current road wheel standard.
Make sure the frame has threaded eyelets to accept fenders, and preferably, a rear luggage rack. You will need to transport stuff and it is too far for a heavy backpack.
Budget for some accessories and kit:
Helmet, lights, lock, repair kit, rack, fenders. Consider some toe clips when you can ride safely.
On used bikes you may need to replace worn transmission (chain, rear sprockets, maybe front cogs) Check wear. You should fit some quality slick road/touring tyres with puncture protection: that or be late on a regular basis.
Clothing: wicking T shirt x3, bright windproof, bright waterproof (separate, even if it says breathable), cycling mittd (for crash protection). You may need cycling shorts, x3. Jeans have thick seams so consider hiking-style cargo pants.

You may be able to minimise startup costs with clothing, but it makes riding easier.