You have gotten a lot of advice!
If you have the option,and if you are using a hacksaw,its true about any of them will do the job.
If you want top quality,Simonds or Starret make nice blades.A bimetal blade has a high speed steel edge with a spring steel back.
Actually a quality hacksaw frame makes a difference.Just look close for rigidity and quality .Look at the tensioners.
On the pitch (tooth count) :You don't want your workpiece to drop into the tooth gullets.Ideal is at least 3teeth in contact with the work.If you can find a 32 tooth,great.28,probably fine.I wouldn't go much coarser.Use a little WD-40,focus n long,straight strokes.No pressure on the back stroke.
You want your barrel held rigid.But,your typical vise offers problems.Crushing it in a vise,obviously not so good.The barrel is tapered,one end will drop.Blocking it up might work,but, If you have access to a table saw,make a 2x4 ...maybe 10 in long,into a vee block. Then you can secure the barrel and vee block to the bench with a couple of C-clamps
There are other ways,of course.
Not everyone has an adjustable die maker'ssquare....but suppose your square has a 4 inch stock.How much is your barrel taper per side over 3 1/2 inches? That extra 1/2 inch is the width of the feeler gage you can shim your square with.Check from both sides.A uniform chamfer with a fine half rounf jeweler file can be close for a chamfer.Something like a 1 in round mounted grindstone can be turned in your bare hnd for a chamfer.
Another thing you might check.I never owned a Mossberg,I don't kmow for sure,but seems like some of their barrels are "back bored".As I understand it,rather than a forcing cone tapering down to traditional bore dia,it does not taper down.The wads obturate to pretty much chamber dia till you get to the choke.
For cheap,that means drawn over mandrel tubing
You cut the chokes off a back bored barrel it might not work right.
And there might be some kind of pattern science in venting off the gas so it doesn't scatter the pattern.Its OK to not like a vented barrel,but they might be about blowing the head off a turkey or something.
Before you cut,study that rib real close as far as how its attached.Oneway was little dovetails and the rib would just float in those.It was soldered on at the endsThe rib had a sort of lug for the solder joint.You cut that off and you lose your anchor.
Thatswhere talking to your smith might be good,ahead of time. Fitting a"dutchman" and getting the torch out with some Hi-Force 44 might be in order.....And sometimes a shotgun barrel does really weird things when you warm them up!
I do think letting the smith do it is not a bad idea,especially if you have to buy tools.