The face mill you have should be OK for your Bridgeport, seems to have some forward axial rake. It looks like it might take a 1" arbor, but you would need to measure it. I just purchased a Sowa 1.5" R8 shell mill arbor and it is very well made and reasonably priced.
I have a Bridgeport style 3 Hp mill, I use different size face mills depending on the material and type of cut. I routinely run a Sandvik RA245 2.5" face mill for aluminum, and just purchased an Iscar (F45KT-D4.00-1.50-R06) 4" to do surfacing on aluminum, I use the 2" F45KT model on steel with different inserts. Never had an issue taking a 0.100" DOC in aluminum or 0.050" in steel even with my previous bench mill (also 3 Hp), and the finish is almost mirror smooth with the RA245. Some of the newer inserts and the different rake angles reduce the Hp requirement and also give very nice surface finishes. The face mill size limitation may be more an issue if you are Hp limited, but a lot of the newer face mills and inserts take a lot less Hp. Best size I would say is a 2.5" unless you have the Hp and rigidity to swing bigger.
I prefer to have a separate shank and head, I can use the same shank on different heads and the head is replaceable if damaged
. If buying new, I would look at the Glacern FM45 face mill series and the Shar's 45 degree face mills for surfacing, for step milling I use a smaller Iscar APKT insert shell mill. Most of my face mills I purchased years ago when a lot of shops were closing and liquidating stock, so about 10 cents on the dollar of a new one.
https://www.glacern.com/fm45
http://www.shars.com/3-45-degree-face-mill-seht-insert-1
Inserts are specific to the material, so you would need to choose the inserts based on the head used and the design/insert parameters. If facing aluminum then you need sharp ground edge inserts which will give a very clean cut. They will not hold up well for steel, mixed metals, or heavier/interrupted cutting. The inserts for steel are very different and coated, they could be used on aluminum but the finish suffers.
Sandvik RA245 five insert 2.5"
Iscar F45KT 2.5" and HM90 F90AP D2.00 with APKT inserts for shouldering, both setup for use with steel
Surface finish with the RA245 with inserts for aluminum.