I think you definitely need to meet with the mortgage expert first to see what you can afford. I do have a good mortgage specialist out here in Suffolk I could recommend that was pretty great. We had met with him and honestly were shocked with what we could comfortably afford. He really did a good break down for us. I’m sure they all do but it shows how important it was just so we knew.
As for neighborhoods, def stay in Suffolk if you are looking for best bang for your buck with more property especially. Nassau is nuts price wise. You can mostly put a lineal relationship to houses in LI based on school districts so the better the district the more expensive the house usually. Also taxes are kind of all over the place out here. I live in a village so I have an extra 3k village taxes on top of my 15k a year regular taxes. Very nuts.
Ronkonkoma, Lake Ronkonkoma (can get pricey), Hauppauge, Commack (some parts get pricey), Lake Grove, Holbrook, Holtsville, Deer Park, Oakdale are all central/western Suffolk reasonable middle class but you do have to pay attention to where specifically where in each place.
Places to stay away from are Huntington station, Brentwood, central islip, lindenhurst, Coram, Selden, centereach, wyandanch, Medford, farmingville.
Some higher end places I’d def just look for deals in are Setauket, Stony Brook, Port Jeff village, East Islip (can get deals there), Dix Hills, Islip, Smithtown, Bayport, Northport, hungtinton village.
Closer to each shore gets more expensive. South shore has more flooding problems from my experience than north shore but also has more boating vibe. North shore has more trees and more historic, older houses. We are in the north shore in port jeff village which is off exit 62 off expressway and north until you hit water butit is a pain getting back to the middle of the island lol.
Feel free to ask any questions.