August and September is a wonderful time to visit Europe. For Europe, you would require to apply for a Schengen visa from VFS. You can do it by yourself online via the link or get help from a travel agent to fill out the details. Basic paperwork is required (bank details, IT returns, proof of travel etc) to obtain a tourist visa.
There are plenty of travel agents to choose from. 50+ Voyagers or Veena World are two options you can look into because they cater to slightly older travellers though they are based in India. There is of course the likes of Thomas Cook, Cox and Kings and SOTC that can cater your travel experience. You could look into Gate1Travel for international groups. They have good packages which cover the countries you are plannin gon visiting.
You haven't mentioned where you want to travel to in each country but on an average, a three-star accommodation on a twin-sharing basis would be about $80-130 a day. Then location transportation, food and amusement would be about another $50-100 depending on your style of travel. As you want to use bus and/or train to travel, instead of investing in a rail pass, it is my advise you book individual tickets when going from one country to the next. You can book indiuvidual tickets on Rail Europe too.