Reddit mentions of Nemosine Singularity Velvet Black Fountain Pen - German Medium Nib

OK, that is the basic, clean package. There are a lot of pens that will meet your needs, as others have said, the Pilot Metropolitan is a really nice pen, and will work very well, it is a solid win, and is recommended a lot because it is a very nice starting pen. Good looks and writes well.

Alternatives that would be good are the Nemosine Singularity medium or fine nib (I would avoid Extra Fine for a beginner). If you like the shape, the Lamy Safari is a pen a lot of people like, I don't think they are the best, but they are well regarded and reviewed.

There are others, Parker IM, Cross, etc. I also really like a lot of the chinese pens, but really think you might want to get down the road before jumping in on those in general. The only exception might be the Jinhao x750, but it is a larger/heavier pen.

Get a converter with whatever pen you buy (the Pilot and Nemosine come with converters, the Nemosine has a nice screw piston converter).

Now, get some ink. You are pretty good on budget, so if you want to go all out, get some Pilot Iroshizuku Take-Sumi. This is an expensive ink, but one of the nicest inks you can get. It is a luxury to use, and the bottle is exquisite. If you get this ink, you have hit your budget.

A little less expensive ink, but really good, get some Noodler's Black, EEL Black, or X Feather (if planning to write on really bad paper).

Hope that helps, you will get a nicer kit than the package above. If you want to add a journal/sketchbook Pentalic works well with fountain pens for cheaper than some of the other brands.