Vocal Microphone- my voice is nasally and perhaps not quite as "refined" as I would like (sort of like Liam Gallagher's). Have been working with a vocal coach and sound fine live.
There is no "one size fits all" solution - you're going to have to try some and determine how it couples with your voice / instrument / etc. The Beyer M-160 is a great tool... you should plan on giving it a shot. With your $1500 budget restriction I would suggest you look on the "local used market" [local Craig's list - etc.] and DEFINITELY "try before your buy" and do your best to ascertain if the tool will fit well with your voice or not.
Rack EQ
Rack Compressor
Rack Preamp (if needed - meaning if an external pre at a modest price point would make a difference)
Again - tough to say. Speck Electronics makes a really excellent equalizer in the like $6-700 range... if I remember correctly its called the "ASC". The beauty of this little gem is that it is a totally "professional grade" tool and a unit you can use and love for many [MANY] moons to come... its not like most "Banjo Mart" crap that you'll outgrow in a year or two... its a solid tool that can last you a career. Its in a 1/2 rack format... so I'd suggest you get a "rack tray" and some Velcro
® to mount the unit [that kind of mounting is for home use - don't try to tour with it mounted like that!!]
Compressor wise - FMR Audio makes some seriously inexpensive and some seriously killer quality stuff. The RNC [Really Nice Compressor] is about $175- and sounds like a grand... the RNLA [Really Nice Leveling Amplifier] is about $225 and reacts more like an LA-3A / LA-4 [a bit smoother... though the RNC is "Super Nice" mode is pretty damn transparent].
If you can budget $475 to this part of the equation then the FMR "PBC-6A" is a really sick / excellent professional tool that you will also covet for a lifetime / career. It has a few extra features, is completely balanced in and out - has some pretty ill linking capability if you get a second unit [linking capability that is far and beyond the capabilities of ANY other stereo compression device - regardless of price!!]... and has "side chain filter" options as well as an internal set of detector path HPF's available at the touch [or touches] of a button.
On the whole - $1500 isn't a hell of a lot of money for professional tools which is why I'm sure you will find few responses on this forum. I happened to have worked at a "high end" shop for a few years and during that time we discovered some rather inexpensive yet elegant solutions so I'm able to share those discoveries with you here.
I would also caution you that the guys that work in the "professional audio" department of the guitar stores don't have a hell of a lot of experience with actual "professional quality" hardware. While you can find some good, inexpensive microphones that can most likely suit your current requirements I wouldn't put a lot of stock in the information they spew... most of them got their information either from other guys in the department or reading stupid shit on the internet [like this for example... only stupider] or worse, from a manufacturer's "rep" who hasn't seen the inside of a recording studio from the drivers seat since MCI 600 series consoles were considered to be on the "low end of acceptable" [unlike their current revered status].
I hope this is of some assistance.
Peace.