When i play england i send off a settler as soon a spossible to get Australia since I usually run out of room for new cities prettly quick. It takes a long time to build up but by the time I am in the modern age my little colony is pumping out units quickly enough to open a second front in SE Asia. I do like to play a long game however, usually building up my cities until I get to them modern era to start attacking.
If you like it that way ...
I used to play like this myself, but since I attack earlier in the game I never run out of room to settle.

Normally it's a good time to first attack, when you get your UU[0] (if not later than renaissance). If you have a later UU, than longswords are a good point for your first take overs. Walling and waiting is only my strategy, when i have a late UU and don't find enough iron.
It'll not so much slow down your city development, when you in between build eg. 3 or 4 UUs (if UU isn't in upgrade path of warrior)+2trebuchet in your best production city, even not if you give it Baracks and Weaponry before. If you can rushbuy parts of this stuff it's even better of course.
The advantage of longswords normally is, that you only need to upgrade units you already have and only eventually have to build some cheap archers as your new city deffers instead of them. For those no barracks are needed.
There are several possiblities how to compensate afterwards depending of your outcome after the first war. If you already have a decent lead in science, you can just leave the missing science structures out in this city eg.
PS.: strategy is tested on prince. don't know how it works out higher.
[0] Some UUs suck. I eg. wouldn't take the Babylonian UU for this. If UU is defensive, you're forced to go with longswords for early attack.
PS.: Forgot something important: Building the simplest unit (eg. warrior) and then upgrading is always the best way to get an advanced unit. Compared to building the advanced unit you get a very good return of production for the gold, and compared to buying the advanced unit, you really get good reward for the invested hammers. So always build the simplest unit before it goes obsolete.