Welcome back to film !!! A couple of things:
The white spots are caused by low film volumes on the minilabs, causing the chemicals to go bad, filters to gunk up, etc. Fuji Europe has an excellent paper on this issue, and they have developed modified chems to deal with it. But I assume it is more expensive, few use it. Your best bet is to find a local place that still gets good volumes and keeps there machines and chems clean and fresh. I am lucky to have a local Costco that still gets lots of film - almost all 1 time use cameras. Prices and quality fantastic $1.50 a roll for negs developed, no prints. They did say though that when there machine breaks, its history. That leaves sendout service. Fuji has print film mailers thru BH Photo. Check it out. Goes to Dwaynes Photo of Kodachrome fame. Superb quality.
But for max film bang, you should shoot a few rolls of slide film, and drop off at the Walmart sendout kiosk. 7 bucks and back in about 10 days. They use Fuji Labs, and it all goes to Dwaynes. Perfect quality, unlike what you will ever see now with neg film, realistically. Slides scan MUCH sharper, smoother, with better colors and resolution than negative film. Try 1 roll and you will see, and be wowed by the magic of film once again (sonething that has eluded you so far with neg film given the low volume problems at almost every lab today).