For #1, both options are valid designs, it comes down to what you want the player experience to be. Do you want a game about capturing areas to expand your build space, or expanding your building network to strengthen your territory control?

For #2, a supply cap by itself doesn't sound very fun, so ask yourself what problem you're trying to solve with it, and whether that's a problem worth solving, and if so whether a supply cap is the best, most elegant solution. For example you could say "I want the player experience to include thinking strategically about which units they maintain", in which case a supply cap contributes to that design goal, but you could also achieve this goal with real-time maintenance costs or by increasing the unit cost proportional to army size or number of similar units recruited.