The first time I came over on my visa, I went through the "UK passports and permanent residents" line at Heathrow. I didn't have a problem at all and went through just behind my husband. If you're at all worried, just go through the "Other passports" line and you can ask the IO which line to use in the future. It's been my experience that my husband and I use the same line -- when we enter the UK, we go through the UK line and when we enter the US, we use the US line.
To get your national insurance number, you'll need to call your local Job Centre and request an appointment. Be forewarned, though -- many Job Centres won't give you an appointment until you have a job offer, so you might need to take care of that first.
For your NHS number, you'll just need to register with a local surgery. You'll have a physical and might have to give a blood or urine sample and will fill out some paperwork. The surgery will take care of the rest and you'll get your NHS card in the post within a few weeks.
Good luck with the move, and congratulations!
