Hi Robert
The arrondissmonts are easy to think about if you think about a snail shell( how appropriate!). They start in the center of Paris with number 1, and wind out roughly snail shell like from 1-20. The first 7 are considered most central ,, although there is nothing wrong with staying less central, most first timers enjoying being in the "thick of it" so to speak.
They are numbered, but also have some names, so the 1st for instance is often called the "Louvre area". The most popular with tourists are the 4th ( Marais) the 5th( Latin or student quarter) the 6th( St Germain ) or 7th ( here known as the Rue Cler area, but otherwise considered the Eiffel Tower area, LOL )
I like the 6th myself , but have stayed in many other areas and like them too.
I personally would get two doubles as I think its nice to have two bathrooms. HOtel rooms in Europe in general, and in central Paris in particular are much smaller then we are used to in North America, so that is a consideration also.
An apartment is another option, but one I have no experience with so will not be commenting on.
If you post a budget( in euros) for a room per night many here can give specific suggestions.
I liked the Hotel Eugenie( I paid 90 euros for a nice single that had two twin beds in it, a/c safe and mini fridge) myself for a budget to moderate choice, but I have stayed in about 8 or9 other places also that I could recommend.
Booking ahead often gets better rates, as does staying a three night minimum.