Congrats! Now do it again and win by 1AD!
Specialists/GPs are an important part of the game. However, your need for many and types depend on the game you are running.
Your first goal should general always be to get out a Great Scientist asap. You can achieve this by getting up a library in your cap or a second city with some decent food. Run 2 scientists immediately. The balance here is which city you are whipping early settlers out of which is often your cap, at least for the first couple. A second city can start taking care of settler needs.
The first GS is often used for a academy in your Cap which gives a nice research boosts usually. However, it can also be used for a key early bulb like Maths. Bulbing Maths is not a great value, but it can be valuable if your main goal is early warfare and simply conquering the map asap with little regard to long term research. I usually only do this if I have Philo trait as the second GS will come soon after.
If you are going a longer game no matter the VC a good play is looking to pump out some GSs for bulb strategies for Liberalism. Look to setup a higher food city as a GP farm with growth some that you can pump out some GSs during a Golden Age using Caste System and maybe Pacifism. With 3 or 4 GSs you can build things like Philo, Edu and put a bulb into Liberalism itself if you avoid Machinery. This ploy is often used to get a fast Military Tradition for Curs and some mid-game stompage. But it can be used for other strategies and techs like saving for later expensive key tech for Space or something.
Still, note that if your primary goal is early warfare and running the map like a Pangaea with Horse Archers, the main goal with GPs is putting you in a better position for that effort. So an early academy or key bulb may be enough. Great Merchants are also valuable. Generally in the late game, but they can have early benefits as well. Running trade missions can give some much need gold for teching, upgrades are just staying afloat.
Yeah, Representation is more valuable with the Mids. Doesn't matter much if you capture shortly before victory, but early Representation is huge.
Also, keep in mind that running scientists early certainly have value other than just getting those GSs. It is static beakers. Let's you get some research while not worrying so much about gold.
As mentioned above, you don't have to keep the slider at X% all the time when you hit deficit research. Try running 0% research at times accumulating gold. Calculate what you need to finish teching then run 100% research. Ofc, once you have Currency you can trade techs for gold and resources for gold per turn (GPT). Always make sure you are trading extra resources for gold - that really helps. Heck, I'll even trade copper or horses to an AI that is not a worry, if I have iron, or single (non-granary boosted) health resources if I'm healthy enough. Anyway, it will take time but you will get used to the sliders.
(Keep in mind that if you look to HA rush you want to get it going asap. You only really need 3 or 4 cities at most to get it going and sometimes don't even need writing first, especially if you have a good commerce resource like gold to work or some early cottages)