It might help us a little if you give us an idea of what nation you like to play as. Obviously each Civ is geared up towards achieving certain victory conditions slightly easier than others but of course, all VC can be achieved with any civ.
There's a couple that I like to play as. I like playing as China, Greece, Ethiopia, and Egypt. I feel like they're either geared up pretty well culturally or scientifically.
From your initial build order it sounds like you take the Liberty tree? Have you thought about going Tradition? Food is the key in this game and Tradition can really help with this. Plus you will bag the monument for FREE.
Well right now since I'm trying to do a game with China, I just started going for a bit of the Honor tree. I did it mostly for the free Great General that pops up if you go for one of the policies on Honor. Most of the time though I just go for Tradition though, but by the time I complete the branch I'll still be off pretty bad considering how long it would take to get all the policies on that branch. As for the culture building, I never realized just going straight for that one could solve my problems with the Monument. I'm going to guess that I should still build the Monument in my first city then try going for it for when I get my other cities built right?
At King you can easily grab the GL and one or two other early wonders also although if you step up beyond King this will become harder and harder. I would usually go SCOUT, put some turns into a worker, build the shrine to get the faith going early, complete the worker and then the GL. The worker can help with chopping etc. Just make sure that when you complete the GL you can choose either Philosophy or Iron Working as your free tech as these are still fairly expensive at this point. Don't forget to settle the first GS and make sure you lock down that tile inside the city view.
Yeah I went with Philosophy because of the way that the National College opens up when you get it and because as you said it was fairly expensive by that point.
Anyway, back to one of my earlier points. Food is key. Always aim to build cities on fresh water sources, for example a river. Get your farms up as priority (farms next to rivers), improve food resources, build the water mills and granaries. The aqueduct comes free when completing tradition. You could also consider aiming for Civil Service as this increases food too. Food, food, food. Always think food

Your newly settled cities will then get FREE monuments and aquaducts so your initial build order can consist of water mills (extra production), granaries, shrines and libraries.
So this just brought up another question for me. This means I should never automate my workers and settle where my advisors think I should be settling in? Most of the time they're never around any rivers and most of the time when I automate my workers they don't really go for the farm building near the rivers and focus a lot more on my luxuries than improving my tiles.
If I take off the automation, how am I supposed to know what to build on where? Farms near rivers but what about trading posts and all those other improvements? Are forest and jungle tiles really something I want or not?
RE the scoreboard. Nope. Mean's nothing, not really.
Hope this helps a little.
Oh ok thanks then
Feel free to post screen shots of a play through every 15-20 turns or so for better advice.
Alright thanks then I guess could you give me some advice on how I'm doing right now then?
I was thinking of building a worker next since I had recently just expanded my city to that second one.
How, exactly, are you getting wrecked? If you're getting DOWed early game and constantly get destroyed militarily, then that's one issue... If you're just behind on tech/money/culture, that's a whole other issue. In higher difficulties (past Prince), you WILL be BEHIND the AI in the first chunk of the game; what determines a successful player is eventually breaking even and then getting ahead of the AI. Try not to be discouraged if you seem behind early game, as the AI gets bonuses past Prince level that let them essentially get a head start that can be overcome.
I get destroyed militarily. I'm always getting DOWed early in game when there's always other people with a better military than me wanting my land for some reason. And alright thanks, I thought I was doing something wrong since I'd look at the scoreboard and see that I was way below all the other opponents
The Great Library becomes too risky at higher difficulty levels. Of course, saying that is irrelevant if you don't plan to play past King, but I would suggest ignoring that wonder; the only early wonder I'd honestly go after is Stonehenge, and that's situational in itself. It's better to either build more cities or more military.
Tbh the highest I see myself going up to is Emperor since anything else higher than that seems way too hard for way too little pay off imo. And doesn't Stonehenge just give you faith points though? In early game I could easily just keep an alliance with a religious city state or build a couple of temples to get to my religion then just buy a couple of more buildings later to wrack up for my Great people.
Buildings aren't as powerful as you'd think; early cities only really need libraries for the National College. Build Walls if you feel a city is a target. Monuments aren't a necessity, although having one in your capital early on IS a good idea (but don't neglect expansion or military!).
I thought more buildings = better early in game since growth and everything.
If military is an issue, focus on having some Archers or Composite Bowmen around to handle any incoming armies. If there's no risk at the time, it's a very good idea send one of them out with a warrior/scout/spearman and break some encampments for city state bonuses. You may feel that making military sends you behind - and if you do nothing with that military, then it will. Early war is usually a bad idea (puppet/annex unhappiness is overwhelming early game along with how being spread too thin can send you backwards and make you a giant target for other AI), but later on in the game if you feel stuck or have an army waiting around, sometimes it can be very beneficial to take some cities from your neighbors.
That's the thing though most of the time I have a big army when I do get there and I don't do much with ti besides just having them stand around to do defense around my cities since I know the AI ALWAYS has a larger military than I do.
Score is just a baseline; being behind in score doesn't necessarily mean you're losing. You should be behind early game and ahead late in the game, generally; even then, though, a nicely planned and timed declaration of war towards the "runaway" AI civ with a score much higher than yours can turn YOU into the runaway civ.
Honestly, playing peaceful makes the game more difficult. The easiest way to win the game is Domination.
That's great to know about the score then I felt I was doing something wrong since I always see the AI with a way bigger score than I have
And I did try a Domination victory, but that just really didn't feel that fulfilling to me when I did achieve it. I felt like a lot of the challenge was taken out, which is why I would prefer to go for a more peaceful victory approach then just conquering the entire world