Welcome to the forum, ovahjay!
First things first? Your questions are really broad so it will help if you can narrow the field. For instance, Italy is a long country so trying to do it top to bottom and everything in between in 2 weeks isn't realistic. So, the first thing your group should do is determine WHERE you want to go. Those wheres may also need to be culled to fit into your 14 nights or so. Oh, and you want to count your time on the ground in Italy in nights versus days, and understand that every location move you make will eat TIME.
What can you tell us about your group? Have any of you traveled abroad before? If so, where? Approx. ages? Any of you have mobility challenges? What are your collective interests? What sorts of things do you want to see and do?
Starting at the top, the most common cities to fly into will be Milan Malpensa (abt an hour out of the city) and Venice. I would probably choose Venice unless you have no desire to visit that city. Flying home, I'll say Rome but explore ticketing prices from where you are.
Getting around in Italy: trains are the most common method, and usually the most efficient. With 4 of you to split costs, there may be opportunities to use private drivers, depending on where you're going. A useful primer for train travel:
https://www.seat61.com/train-travel-in-italy.htm
Hotels: I use booking.com, as do quite a number of other forum posters. You can filter per price, location, desired amenities, ratings, etc. You can also browse the RS forum history for recommendations using the search box at the very top of every page. IMHO, there's no such thing as 'best rates', just best choices for location, amenities and ratings within your price range. Be sure and browse the reviews.
https://www.booking.com
You might want to consider apartments, although newbies abroad often feel a greater sense of security with the 24/7 desk staff many hotelsprovide. Apartments almost always involve cleaning fees so are not great choices for short stays, and what they call a 'bed' can be a fold out in the living room. That may not bother you but... Your group of 4 may want a little individual privacy now and again as well so think about if you want to be ALL together, ALL the time? Some of you may be early risers, some of you may be night owls.... you get the idea. Different strokes are also a consideration when it comes to moving around: you're only going to do that as quickly as your slowest dawdler.
As well, you probably want to divide and conquer! For all sorts of reasons, one person shouldn't take on this entire task! Duties split amongst you can be researching train tickets, attraction lists and advance ticketing, accommodations, meals, etc. Also, agree IN ADVANCE how you're going manage the costs amongst you. This is really important as there will be a point in time when the stake has to be firmly in the ground as far anyone backing out. This can include everything from non-refundable attraction tickets, accommodation reservations and train tickets.
You should all make sure you have health insurance with good coverage abroad as well. You may need to purchase a travel policy in addition to what you have.
Just a start! So start drilling down to where you want to go and give us those thoughts, and tell us more about your gang? You'll find oodles of help here!