Anything else I should attach other than this?
You should include all of the same evidence you included for your first application updated to their most recent versions. These would be your evidence to support your personal circumstances along with your bank statements, salary slips, and so on.
May be a apologise letter for my previous application or anything else?
Refusals do not warrant any sort of apology, it's not appropriate. You paid for them to consider your application, and they did it... end of story. If you want, you can add some text to the "Additional Information" section along the lines of...
In my previous application, the ECO made an assumption that was
unfavourable to me, namely that my relationship to XXX company was
dubious and therefore suspect. This was the sole objection mentioned in his refusal notice. Accordingly, I have taken steps to assure that my
relationship with XXX company is now set forth explicitly in the
documents accompanying this application.
This was the only deficiency communicated to me in my refusal notice;
deficiencies in my other evidence was not mentioned, but I have
taken the steps to update it where necessary to assure you have
the most recent versions.
What should I mention with my approximate travel date ( its flexible for me, I've got to know should be at-least 2 months from my visa application)
You should give a date not more than three months from your application date. Hopefully your employer in the UK put some dates in your invitation letter (if not, then there's a problem with your employer).
I attached my bank statements in last application, Should I again, if yes, what are the minimum funds I'd need to show?
There is no minimum amount. They work in proportionality of your income to the cost of the visit that you will bear personally. If it is out-of-whack they will refuse because they will not believe that you are a genuine visitor (genuine visitors do not deplete their financial reserves to make a short visit). I assume that your deposits are dovetailed with your salary slips from the UK employer who invited you. Any other cash flows need to be carefully explained.
Is it the right visa type / time to re-apply?
As we already pointed out over here, you will be applying as a Standard Visitor. The best approach is to study the guidance and be sure that everything mentioned is covered in your evidence. Secondarily, you can study their internal guidance to see what they will be looking for in your application.
For your question about if it's time to apply, you can make a fresh application any time you think it will succeed. There is no "cooling off" period following a refusal.