Likely early on it is a good idea to expand laterally and ensure enough habitable planets are under your control, but at one point you need to focus on spamming colonies for density. This is based on merely my first play through though, so may need to experiment.
Going by the ship guide linked, your average numbers will likely dip as there is a good chance you will be using weaker weaponry, but you will be able to directly counter the opposing fleets ships.
Yeah, this is basically how I'm experiencing the game so far.
Phase 1: Explore a lot, build like one frontier outpost in the best place you can reach for resources, balance mineral and energy production on your homeworld. You need significant mineral income but you just need to be net positive in energy credits and you probably don't want to dip below +2 or so in influence. Probably try to build a second science ship to explore faster.
Phase 2: Start colonizing planets of your type, pretty slowly because colony ships are expensive and colonies cost a lot of energy credits. Micromanage buildings. Don't colonize too tightly, you want to spread out and get a lot of territory for mining, but you also want high-quality planets (good resource squares, lots of room, not too many blockers). Build a second constructor ship and start mining everything in sight.
Phase 3: Get an additional colonization tech. Your mining stations are kicking in and you're producing more resources, so start cranking out colony ships. Make a sector or two. You don't care any more if your planets are shitty because they're going to be your governor's problem, not yours, so just grab them and delegate them immediately. Keep mining everything. At this point your second science ship is probably going to get redirected to special projects instead of further exploration.
Phase 4: You are suddenly super rich because everything everywhere is mined. Colony ships are no longer expensive. Put up starbases literally everywhere. Your fleet cap pops hard so build a bunch of ships. You are ready to conquer the universe.
The one thing I really want for Stellaris is the ability to find out what ships your opponents are generally building without having to lose a fight with them first to find out. That seems like a weird gap in the design -- if you're going to have rock-paper-scissor ship building you probably need to have some kind of scouting.