I feel sympathetic to your cause, because like you, I was confused at all the jargon and technical stuff involved with transitioning to a stick. Here’s the best I can help you. If you need any more assistance, drop a PM.
1. Can anyone recommend me anything better, or is this Hori the safe bet. (This will be my first stick)?
Before we get into the details, do you want to go US-style or J-style? While there are a dozen different varieties and types, it pretty much boils down to these two. If you are getting a stick for the sole purpose of familiarizing yourself with it, look at the sticks that your local arcade’s cabs use (more specifically, the games you play).
As far as stick selection, the bottom line is that you get what you pay for. Personally, I would drop the fifty extra bucks on Hori’s best stick, the Hori Real Arcade Pro (HRAP). From there, swap the stock buttons for Sanwas and you should get the closest configuration to a Japanese cabinet.
For US-styled sticks, your choices are sparse: either go MAS or custom.
2. Also, will there be any lag from using the converter with the stick to play on
Again, depends on the quality of the converter. I use a Magic Box (PS2 > Box) and it gets the job done. HOWEVER, once you reach the optimal level of familiarity with your stick (takes a bit longer than a month), you will notice the very small “insensitivities” that all converters give.
3. And how well will this stick work with the games I play?
All personal preferences.
That being said, there are crowd preferences. Different crowds prefer different configurations. The MvC2 circle is pretty much exclusively US-styled. The Gear circle is opposite (J-styled). The SF circle goes either way. Again, depends on your priorities.
4. Are Sanwa and Seimitsu parts used in this stick, and if not how hard would it be to add those parts into it?
In the stick you listed, all parts are Hori stock. Modification is possible, but the mod for that particular model is much more complex than the HRAP.
5. What is the main different between HRAP and Hori?
Hori makes the HRAP.
6. Willing playing with the arcade stick at home feel the exact same as playing in the arcade? (I play at the local arcade a lot and I find it hard to play since I’m used to using Xbox/PS2 controllers)
Depends on what you chose. What you selected was a Hori. Hori exclusively makes J-styled sticks.
You are from Brooklyn… so I assume you go to CTF? And IIRC, the majority of cabs there are US-styled (I am not from NYC, can any native correct me on this?). If you want to get this stick to simply be adjusted to CTF’s cabs, then I would invest in a US-styled stick.
Hope this helps.