I suppose it goes without saying that the more leagues you run the slower the game will process but what I want to do here is maybe offer some LLaMa perspective.
Using the above screenshot as an example, I've been to the LLMPicker and the llamas have given me a team from Finland. In years gone by I would just load all leagues from the game and suffer the slowness in the name of realism but more recently I think to myself "How do I want this save to go?" and in this particular save I quite fancy the idea of a Scandinavian setup that gives me options in and around the area i'm starting in.
With this in mind I've loaded all of the Nordic nations and I've also loaded the top flight leagues of four of the major nations from Europe to keep the European competitions like the Champions league competitive over time.
From what I can gather from talking to others about how they set up their own games most people even on less than capable machines tend to opt for a large database of players.
I myself always use a small database as I personally find the transfer market is more active and of course less players equals faster processing times. Even with a small database, as soon as the first youth intake comes there will be plenty of players in my opinion.
If you are playing in a deep league (England, Sweden etc) and starting at the bottom do you need to run a large database and lots of other leagues? Chances are you won't even be able to scout outside your own nation to begin with anyway and you can always add more leagues if/when you reach the higher levels and of course you can always take some away.
Lastly I often see advice around the internet about running leagues as view-only. In my opinion this is pointless. All this does is give you league tables for those leagues and no extra players, also, these league tables will be primarily simulated using the clubs reputation much as they would if they were non active.
I would always argue that it is better to use your precious processing power to run one more active nation than running multiple in view only.