OP,
Well, not regarded as at all 'weird' around here for a newcomer simply to introduce themself, thank God!
Suss out whichever neighbour looks the most approachable, avoid times they look particularly rushed, friendly smile and a "Just wanted to introduce myself...I'm X, and we've moved in at number Y" is all you need, I'm sure.
If your new neighbourhood seems so welcoming, go with your instincts: in time, you'll get a feel as to whether Mary 2 Doors Down would jump at the chance to pop round for coffee/ to meet your DH, but that Ann The Other Side is far more private, and wants to keep interaction minimal.
If, for any reason, you don't feel able to approach people so directly, then maximise chances for passing locals to strike up casual conversation with you instead (or even just to exchange a neighbourly nod and log your face for recognising in future).
Be outside as often as possible, esp. in early evenings/ at weekends...summer's ideal!
If you have any street-adjoining garden to be pottering around in (or even a tub/ hanging basket/ pavement hedge), then that's an easy one...
Nice comment to neighbour dogwalkers/ any parent of small DC, whilst fondly smiling at their dog/ toddler? Be a regular at the nearest shop?
Maybe a follow-up with "Oh, btw, would you know the best place round here to ?"
Good luck...I like the sound of your new community 