I am not a tax accountant, so take any numbers in my post with a grain of salt. All the below assumes all your income is from regular fulltime employment only.
Tax bracket (Steuerklasse) does not affect how much taxes you pay. Only at what time you pay them.
For example, if you have Steuerklasse 1 you pay the maximum up front. If you don't have any reductions, that's the default, you need to do nothing, your tax declaration is considered "done", since you already gave them the maximum amount. Lets say you marry and your wife stays home with the kids, then you'd need to pay less taxes overall. If you keep Steuerklasse 1, you still pay the same amount every month up front, but you get some money back when you make your tax declaration, because you can deduct something when you have dependents making less money than you do.
Since marriage (or other relevant circumstances) are rarely spontaneous, it seems a bad investment to just give too much money away each month only to recuperate it an the end of the year. It would be smarter to just give that amount of money that you actually owe. So if you already know that you will have to pay less than the maximum (because you are still married and plan to be for the whole year) you can get a different Steuerklasse where you pay less every month.
But in the end, Steuerklasse only says how much you pay every month. The amount you owe in the end does not change. If you paid too much over 12 months, you will get money back, if you paid too little over 12 months, you will have to pay the remaining sum then.
If you are Steuerklasse 1, a tax declaration is optional. They already have your money. If you claimed any other Steuerklasse (and paid less than the maximum) you have to make a tax declaration, to provide proof that you indeed didn't have to pay the maximum.
Assuming your tax declaration is optional, you can make tax declarations up to 4 years back. The amount you get back does not change with the years, apart from not having the money in your bank, there is no special drawback for doing it late.
Does Steuerklasse have a massive effect on what you get back?
In a way. If you pick the wrong one, and overpay all year long, you get more money back than a person that did not overpay. But the money you get back is money that was drawn from your account and that you did not need to pay in the first place. So who got how much back from a tax declaration is rarely a good measurement. It was theirs to begin with. It does not say anything about how much taxes a person actually paid.
Since no tax declaration of couples, maybe even with kids, is uncomplicated, it's nearly impossible to get exactly the correct tax bracket. There is only around 5, compared to untold combinations of factors that lead to tax deductions. Since you have to always overpay, couples tend to get more money back from tax declarations than singles, who are probably pretty close to the default. But again: that was their money to begin with, they overpaid and they get it back now.
Would you recommend me to go for a Lohnsteuerhilfe? Would that affect my result as a newbie in this topic?
Yes. Any kind of tax accountant is fine. They will feel seriously bored doing a single's taxes, but so what. They get paid for it. They will be able to give you ideas what you can deduct. For example anything for a job (commute costs etc). Anything you used to get a job (traveling to/from interviews, maybe special preparations, photos you had taken for your CV etc). The point is, they will ask you whether you have done this because they know it's deductible, while you'd probably never think of it and not deduct it. They probably need one hour of time, for something you'd do a worse job and need 4+, so that's probably money well spent. At least do it once, so you see what you'd need to do. If you decide to do it yourself next time, at least you can compare results.