In other words, this means that upgrades are only viable if you have many ships, as the impact of upgrading is bigger than buying an additional ship?
Yes. If you only have 5 long range frigates, adding one more will give you more firepower and hitpoints than a 5% increase to firepower or shields or hull. You get more fo ryour money by adding an additional ship. In contrast, if you have 60 of those ships then a 5% increase to a stat might be a better buy then adding an additional frigate. Sometimes a good time to do your upgrade is when you've bumped up against the top of your fleet supply because now you'll need to take on an additional tax burden and do fleet research to get more ships. At that point it might make some sense to do a little research to increase firepower, shields, and hull, especially if it's just first, second, or third tier research. Of course, it's very difficult to formulate an exact rule for what makes the most strategic sense; it's going to depend on your exact situation.
"Don't get carriers too early though. They are expensive and you won't have the funds to deploy them."
Could you elaborate on this? Why are they so expensive? Do you mean purchasing them or in terms of ongoing costs? Why are carriers so good, you only get two squadrons, which is not so much in my view? Do they really do so much damage? What is the preferred ratio of fighters and bombers in any given fleet with carrier-type of ships? Sorry for asking so many questions, but your answers so far have been very useful and I think more people could use this type of advice.
They are expensive ships and they can be easily neutralized by opposing carriers with fighters, cheap flak frigates, or capital ships with anti-strikecraft abilities (like the Halcyion Telekinetic Push). If your opponent has lots of strikecraft then you're going to need some with your own fighters and flaks. As with everything, sometimes it makes sense to have them and sometimes it doesn't. Strikecraft are nice to have if you want to kill an enemy's construction (structure-building) frigates when you enter a gravity well to attack or if there is some specific ship or structure you don't want to approach closely that you want to target from afar.
Personally, I view strikecraft as being useful primarily as a counter to enemy strikecraft and for killing enemy construction frigates. I don't regard them as a primary fighting unit. Sometimes you will encounter (human) opponents who will pump out swarms of strikecraft which can be annoying and a pain if you do not already have the counters for them. When that happens you need to quickly put up your own counters (your own carriers with fighters and lots of flak ships). As a general rule it's cheaper to counter strikecraft and to neutralize them than it is to build the amount you need for offensive purposes.
Bombers are powerful and great for taking down structures, starbases, and capital ships if you have a sufficient mass of them, but they're easily countered by enemy fighters and possibly masses of flak frigates. However, if you have a huge swarm of bombers, they can kill things before they themselves are killed, which is great if you want to kill a specific enemy capital ship. However, once the enemy's fighters have killed your bombers they will then have air superiority. Strikecraft can be more useful and less likely to be countered early game before people have put up diverse fleets. One common strategy people are using now is to quickly pump out two carrier capital ships at the beginning of the game so that they can engage nearby opponents with 6+ strikecraft before they've had time to put up their own flak frigates and carriers.