To the person who inspired this post, I thank you. While answering your questions, I also reminded myself of why it is important to dress in the ways that I was myself questioning. If you will forgive me for posting my answer to you on this blog -- I feel that it is important to share this with others like me and you who have questions about what Chassidic dress is required, what is not, what components are important, and what attention needs to be paid to the details when dressing, and why each piece of dress is important.
The karpota and belt are worn by a married guy, and I'm not yet married, so all I wear is the beard, the tzitzis, and the black suit with a white shirt -- this is on the days that I'm not wearing a colored shirt which chassidic people also wear, or jogging pants and a tee-shirt which you'll almost never find chassidic people wearing.
...There is no need for a black hat; a double head covering (i.e. yalmukah plus any covering, even a baseball cap) when you pray will suffice according to Kabbalah which is where the hat custom came from.
As for the gartel (the belt), some people just use a stretchy string to tie around their waste to hold down the tzitzis. According to kabbalah, this also serves to separate the bottom half of the body and its desires from the heart and the top half of the body. I don't do this, but when I am married, I will wear a gartel when I pray, which is the custom.
The karpota (long coat) serves no purpose except fashion as far as I know. There is a kabbalistic concept of wearing a silk robe, [and I don't know the reason for this], but karpotas are usually not silk, and some people wear a silk karpota under their regular karpota.
So as you see, the type of hat does not matter. The jacket is just a jacket as far as I'm aware and it serves no purpose except to look nice. The suit is just a regular suit, as one would find in any suit store -- no particular style for any of these things is halachically necessary, and as for kabbalistic reasons, which is what I think you are asking about, the important thing with a hat is to have the double head covering when you pray, even if you use a tissue under the yalmukah (don't let people see because it looks dumb) or a baseball cap over it.
If you want to get fancy, there is a concept in Chassidic thought of Chesed (kindness) and Gevurah (strength / stringency), where the right hand side is a manifestation of Chesed and the left hand side is a manifestation of Gevurah, therefore the right side should preempt the left side in almost whatever you do (i.e. put on shirts or jackets with the right arm first, and you put on pants, socks, and shoes with the right leg first. [You tie the left shoe first, but that is because the tefillin which one should put on every day during prayer is tied on the left side). Other than the tefillin exception, many people are careful to always eat with the right hand and to even look at people focusing through the right eye. This is extreme, but I am answering your question. In line with this, some people sew an extra button on the inside of their jacket so that they can close it with the right side over the left side, which is opposite from the way jackets are typically closed. There's a bit of extremist Chassidic philosophy for you -- but in some respects, for example putting on clothing with the right hand first, this is halacha (Jewish law) and so it should be followed. However, buttoning the right side over the left, looking through the right eye, holding things with the right hand are not requirements and are far beyond any requirement, custom, or law.
But more fundamentally, it is important to always wear the yalmukah (according to kabbalah, even in bed) before you start thinking about all the extra head coverings. It is most important (if you are not already doing so) to wear the tzitzis (according to kabbalah, to wear them all the time even at night, but don't designate the a pair of tzitzis a night garment or else they won't be kosher even during the day; just wear them into the night) before you start concerning yourself about the gartel (belt). It is more important to dress modestly in black and white (although there is NO jewish law requirement for this, it is purely kabbalistic and modest) before you start looking into karpotas or jackets. Any dark blue or black pants will suffice, and any button down white (or colored shirt) will suffice. Men typically wear a jacket (even any blazer or sweater will suffice) when praying. I hope I have answered your question.
Interestingly enough, by answering your question, I was reminded why we wear black and white. It is for kabbalistic reasons. I forgot this over the past few months while I've been ranting and raving about this dogma, I forgot that there is actually a good purpose for this. Being that in my world of law filled with attorneys and fashion-conscious people, I will continue to wear colored shirts from time to time, and I will continue to wear a tie from time to time (which kabbalistically one should not do because it separates the heart from the brain). However, now that I have remembered why chassidic people dress in black and white, I will feel more spiritual when I too dress in black in white, because I will be reminded of why people do so in the first place.
I thank you for this.