Ex army brat and army wife here had over 30 addresses I can pack up a house in an afternoon!
You will need:
Packing boxes
Duct tape (don't bother with crappy "packing tape" it's not strong enough once boxes are filled)
Thick marker pens
Black bin bags
White bin bags
Hand gel and kitchen roll - for quickly cleaning hands as you go so you're not marking eg clothes with dusty hands.
Old clothes you don't care if they end up wrecked, you'd be amazed how dusty/dirty various nooks and crannies you're packing from get! I'd also highly recommend wearing a headscarf!
1 be UTTERLY RUTHLESS about clearing out as you pack! Don't be taking boxes full of crap to the new place!
Set up the boxes for the things you will be taking with you, but also have ready to fill:
black bin bags for rubbish
white bin bags for stuff you're donating to charity
2 decide what you're going to NEED to be using until last minute and will want to unpack as soon as you arrive at new place - kettle, mugs, cleaning basics, toiletries etc and set a small box aside JUST for this stuff which is clearly marked - inc warm pjs even if weather warm JUST IN CASE being too warm is easy to deal with just by stripping, opening windows etc, if you're too cold 1st night in new place and haven't warm clothes prepped and can't work out how to turn bloody heating on it can be miserable!
3 pack by room - makes it much easier to unpack and find things at the other end. Mark boxes clearly
But DON'T pack in boxes important and difficult to replace documents - if you haven't already create a folder that contains birth and marriage certificates, passports, bank books etc and that goes in a handbag/suitcase and STAYS WITH YOU. I'd also apply this to difficult to replace precious photos especially of loved ones that have now passed, if they're in photo frames take out the frame for now and pack the frame but you will be heartbroken if they are lost/damaged.
4 don't pack boxes full of solely heavy items, mix it up or else you'll have boxes that are way too heavy to move easily eg no boxes FULL of books, photo albums - have a few books at bottom of box then the rest lighter items like clothes, linens and cushions
5 yes to packing fragile items in with clothes/linens etc though as generally works better than specialist packing too
6 DON'T get distracted reminiscing, keep moving keep packing - having upbeat music on really helps
7 if possible do a clean, carpet, paint freshen up and curtains/blinds sorted in new place BEFORE you move in. At the very least as pp said get measurements.
8 Yes, re contacting all your bills companies - get onto that ASAP it can take up to 6 weeks with some companies for the new info to get through to all depts - go through last full months bank statement to create a list to call and tick off as you've called them. Request final letters sent to NEW address where possible.
Also worth paying for mail redirect especially in these times of identity theft.
Inform everyone who normally writes to you - inc birthday cards etc - of new address and ensure they've RECORDED the new address - one of my grans used to be murder for this and would be sending birthday cards with cash in to old addresses!
If you are moving white goods use professional removals as they will know the correct and safe way to move things like washing machines.
Good luck