6K Man
Bureaucrat
Settle on Stone... maybe.
AT what level of play do you play? At higher levels it's very difficult to connect stone before the AI has already completed SH.
Having a very productive capital vs unproductive border cities seems to be a common reason to centralize production in the capital by way of building SH instead of monuments.
This is actually a huge trap in reasoning. New, small cities have basically nothing else to do at the start of the game except produce warriors before granaries come online. Too early for barracks. Settlers / workers are weak builds in a city just getting started (need to grow on available tiles, low hammers means stunting this growth for a long time). You only need so many warriors to spawn bust, so it's nice to have another option.
The other main trap in reasoning is thinking "well I'm going to build at least 6 monuments this game, so a SH will save me hammers". Everything you do is an investment that will pay itself off, but the returns from a settler and worker are astronomically more exponential than SH. So much so that this remains true even if you want monuments in all your cities (char), start on stone, are IND, etc.
Going for SH only really makes sense if some of these conditions are met, and SH goes very late, the odds of which depend on the difficulty level.