What are the storage and lodging capacities for the towns and cities in the game?

For storage, The largest city is Calpheon, this has the most building options, and is centrally located if you plan to stay on the "life side" of the map.

Another option, which most players seem to prefer, is Heidel. It is smaller than Calpheon (making it much easier to navigate), and still has plenty of options for building opportunities. Heidel is also more central to the entire map, making accessing every area a bit easier.

As for the lodging side of your question, you can have workers Live in Velia but still do work somewhere else entirely, it will just take a little bit longer. So again, Calpheon or Heidel will be your best option (there's no reason not to do both, it's cheaper contribution point investments that way anyway)

You can always permanently increase the storage/lodging units of cities with pearl/loyalty items as well.

Personally, I tend to stick around Calpheon more than Heidel, but that's because I do more work in Port Epheria nearby.

All the inventories are limited at 192 slots. And all major cities can get to that.

Regarding lodging the largest you could get is from Calpheon, followed by Heidel, Altinova and Valencia (didn't count the exact the number but they looked rather similar to me), while Velia is totally worker deprived (for Balenos area you need to use workers from both Olvia and Velia to properly cover it).

As a side note thought (not requested by the question but I think is really important), you should consider the CP investment for what you need, and what nodes you want to send your workers to. Heidel is popular because Heidel lodging is really cheap (1 cp / lodging, even less for some). Valencia and Grana for example are really expensive. Also Heidel is near center of the map so you can cover more ground with it. There are more things to consider when choosing investing options.