What is the optimal way to publish the first scientific article? I am a doctoral student (economics) and I'm about to finish my first scientific article.
Unfortunately I have no experience in publishing.

Can someone explain to me how best to publish this article?

I have some questions to which I am looking for an answer.

A) How do I search for the journals and how do I contact them or submit my article?

B) How do I recognize good journals and is it realistic that I can publish without any scientific reputation in a good journal?

C) Should I have the article professionally checked beforehand? (I am not a native English speaker)

D) How long does a normal process take from the first contact to the publication?

E) What are the advantages and disadvantages of an open-acess publication? I see this positively, because I want to share my results with as many people as possible.

F) What costs will I normally have to pay?

A kind of checklist for publishing would also be good. I think there are many more points I have not thought about.

I hope that someone can help me with his experience. Also I am grateful for further hints about things I have not considered.

Many thanks in advance!
I'm a doctoral student as well with a few articles under my belt. Here's my take on your questions, but first let me say that I would expect your advisor(s) to be able to answer those better than me, and they should have a voice in the process as they are likely to be your co-authors.

A-B) You should aim to publish your articles in journals that are on-topic. You can find good, on-topic journals by inspecting your references, since what you reference should be typically good, on-topic articles. The submission process varies but is usually well-explained on the journal website

C) It depends on your level of proficiency in English, but I'd say to ask your advisor to review it and trust his/her judgment of it.

D) Usually a review cycle takes anywhere from 1 to 4 months. A polished manuscript can take only one review cycle, most articles will take 2 or more. My articles have taken between 9 and 12 months from submission to acceptance.

E) Open-access is nice, but will almost always cost you a fair bit of money (in elsevier journals it's around 2000$ i reckon). What i advise is to submit the pre-print to arxiv (which anyone can access) when you submit to the journal, so you get both exposure.

F) Normally in 'closed-access' journals the publication will be free except for over-page fees (when your article is too long) or to have the article in color in the paper version. Over-page fees are a few hundred $ per page usually

My general advice is to take your time to find the right journal, and don't aim for super high impact factors. It's better to find the perfect (but small) audience for your paper than a lot of people who aren't interested in it. Give it to a lot of people in your research group to read and get feedback. Any criticism you address before submission will shorten the time to publication a lot. 

Finally, consider if a journal is the right type of publication. In a lot of fields, conference papers/proceedings are a strong way to show your work and do networking.

Good luck in your research!