OK, here’s some general thoughts from another random EVE player based on everything you’re asking here.
First, welcome to the game! It sounds like you are off to a great start, and kudos to you for trying new things and asking for help. The community here has an (earned) reputation for being gruff and unfriendly, but a lot of us genuinely love helping new players.
So, with that, here is a wall of text that touches on some of what you are asking.
Missions
Lots of good advice here, and I heartily recommend trying the SoE Arc as your next step. That will show you New Eden and build some standing. In the context of building standing for the purposes of running missions, this will certainly help get your feet wet. The topic of standings is, like all things in EVE, extremely complex at first. Here’s a good article that covers the basics:
https://wiki.eveuniversity.org/Standings
Some rules of thumb here:
- Be careful managing your standings, since fixing them can take a lot of work
- Be aware of how derived standings work.
- When doing missions, avoid taking those that pit you against empire factions, as these will kill your standings with them (pirate standings are generally fine to nuke).
- Follow these rules until you have enough experience to know why/when not to
When you start running missions, research them first to know what you are going against. Here is a link to help with that:
https://eve-survival.org/wikka.php?wakka=MissionReports
Weapons
Rail are a great way to go and get started. All weapons have pros and cons and slightly different mechanics. But, turrets require understanding some mechanics such as traversal, angular velocity, optimal/falloff, etc. In addition, make sure that you understand the skill path to train to get the best performance out of your weapons. Here is a good article that covers the fundamentals of hybrid turrets (blasters and rails) so you get a sense of all of that and have an idea of what to train or explore further:
https://wiki.eveuniversity.org/Turrets
Gunnery fundamentals
https://docs.google.com/viewer?url=https%3A%2F%2Fdocs.google.com%2Fuc%3Fid%3D0Bymhje4Rma0GakpmX2x1bUM0ZFE&embedded=true
Fitting
Fitting ships is both an art and a science. It is highly variable, not just on the raw stats of the ships and modules, but also on the skills of the player, what the fit will be used for, and how the player likes to fly. You can take the same ship and fit it completely differently for a kiting PVPer or a brawling PVEer. The in-game tools can help there, but I’d suggest looking into using a tool like PYFA as this offers a lot more information and is generally easier to get around in (once you get the hang of it).
Fitting Basics:
https://wiki.eveuniversity.org/Fitting_Guidelines#Fitting_modules
PYFA and how to use:
https://wiki.eveuniversity.org/PYFA
(be aware that the PYFA article is a little dated due to the changes from API to ESI, but we can help with that when you set it up).
Ships
Repeat after me- “Bigger is not always better”. While getting that newer, bigger ship is a TON of fun, unless you can fly it properly, you will not be in good shape. And remember, that all ships have pros and cons- frigates will struggle against battleships, but battleships will struggle against frigates…unless you know what you are doing and how to fit them. That experience will come, but my point is not to jump into a bigger, badder ship until you really know why you need to do that, understand the trade-offs, and are properly skilled to do so.
And, while I agree with @erg_cz that the Gnosis is an awesome ship for a number of reasons for newer players, I’m not sure I’d recommend it just yet for the SoE arc. As he mentions, you need to have some skills to get the most out of it and it’s kind of slow for some of those long jumps you need to take in the mission arc. For what it’s worth, the first time I did the arc I did it in the Gnosis’ little brother, the Sunesis 
Skills
Ships are fun. Guns are fun. Training those skills is great and you can get some immediate gratification.
But…without supporting skills to back them up, you’re hosed. Your rails won’t help you when you have no cap. You won’t have enough gank OR tank unless your engineering skills are up to snuff.
There are a group of skills called the Magic 14 that are fundamental skills for any pilot. They are not sexy by themselves, but they allow you to train other skills and fit modules that are. And these are important because they apply to any ship and any career that you choose in the game.
https://wiki.eveuniversity.org/Magic_14
I’m not saying to deprive yourself of training the sexy skills to get all these under your belt first, just make sure you don’t neglect these. Slip some of them into your queue in between the fun stuff- I promise, you’ll be glad that you did later.
Things to remember
People will probably disagree with me on this, but these are things I have found to be true in EVE:
- As long as you follow the rules, there is no “wrong” way to play EVE. You do you.
- Fun is infinitely more valuable than ISK. Don’t fall into an ISK grind for too long or you’ll be miserable.
- EVE has no end. Set small, medium, and long-term goals, and don’t be afraid to change them.
- EVE is about the journey. Lots of things take a lot of time, especially training skills. Learn to enjoy that.
- You will die and lose things. That’s part of the game. Accept it now and don’t stress when it happens.
- Ask for help when you need it, and don’t let Bitter Vets like us get you down.
- Always remember…they are just pixels on a screen
o7