When it's running well, it will put a smile on your face every time you get on.
Some reading and resources:
http://vmoa.net/VMX12-Service-Manual01.pdf
https://www.vmaxforum.net/threads/new-vmax-owner-faqs-new-members-please-read.21240/
I suggest changing the brake fluids in the clutch and front and rear brake master cyl's. Also the coolant. Leaking fork seals leave wet deposits on the sliders. If your downtubes are chipped, forget changing the seals until you replace the downtubes. Check Forking by Frank or Race Tech for replacement tubes, they aren't cheap. Your downtubes should be 43 mm (1993-2007). Early (1985-1992) are 40 mm. You could also seek used replacements here in the classifieds, but buying off ebay, you may end up with chipped ones worse than the ones you already have.
Caveat emptor.
How to make a simple, cheap hydraulic system bleeding tool, as well as how to replace a bad clutch slave cylinder:
https://www.vmaxforum.net/threads/clutch-slave-cylinder-replacement.45011/
I used to use a Mity Vac but now I use a syringe. I find for me it's the quickest way to get a good fully-bled system for either the brakes or the hydraulic clutch. It can be a bit messy if you're careless, have some spray solvent to spray down any spills onto painted parts, as the DOT 3, 4 or 5.1 will ruin your paint. I usually remove the faux air filter/gas cover when doing the handlebars' master cylinders.
You can check the rear shaft drive housing for volume in-there, but probably you won't need to change it, though it can't hurt to do it.
Race Tech and Progressive Suspensions offer different fork springs including internal lowering if you happen to be short. You might want to check the air in the front forks. Be aware they fill very-fast from a compressor! About 5-15 psi is the range. If they are empty, it means 1 of two things:
they've leaked-down and need to be re-pressurized
or
you already have Progressive Suspension springs, which do
not need to be pressurized.
Use the search function in the upper right-hand corner to see posts about the Progressive Suspension springs, what they look like, and the appearance of the OEM springs. The search function, and the 'advanced search' function, after the 'search' tab is clicked-upon, are your E-ticket to specific information on subjects you want to research. probably anything you're having difficulty with, someone before you posted about it, and there is a lot of info for the reading.
Race-Tech and RICOR also offer cartridge emulators, which eliminate the OEM damper rods' function and turn fork damping over to wave-washer stacks, which are very adjustable. Changing your fork springs and adding the cartridge emulators when properly-tuned, make a big difference in the handling of the bike.
FYI, I think the #1 biggest change in the bike's handling comes from changing to radial tires. This normally requires a change of wheels, which is $$$$. No Gen. 1 VMax ever had OEM radial tires. However, if you ever rode a radial-equipped VMax bike back-to-back with a bias-ply bike, you would recognize the difference in handling dynamics. Especially at 'lose-your-license' speeds, which can happen in oh, about 10 seconds. The bike becomes much-more stable at triple-digit speeds on radials. Use the search function to find info on wheels and tires of the radial persuasion. FYI, radial tires require a wider wheel to fit the tire carcass best. It's all there, in prior threads and posts, happy reading.
The carburetors have pilot jets in jet blocks, which easily become plugged, from gas tank rust, contaminated gas, and water in the gas. I bet there are more-than a few VMax Gen. 1's out there, which have never had their gas filters changed! If they run, they probably run like you described. You can get an equivalent gas filter at your local auto parts store (take your OEM filter to compare, and buy two), or order a replaceable element one online. Russell makes one and there are knock-offs on ebay. In any case, you want to drain the contents of each float bowl into a container, to see what's in the fuel system. Looking at the gas tank, it should be shiny-clean inside. If it's corroded (rust is evident) or there are deposits then at the very-least, you need to clean the gas tank. It is possible someone already treated the gas tank with a system, which coats the interior after cleaning it. That will NOT appear shiny-clean! Done improperly, (not uncommon), the liner will fail to bond to the tank interior, it will shed and clog your fuel system.
All these things I'm describing, there are many threads to read, just use the search function. It will save you time, work, and $.
I suggest you read about cleaning the carbs, what gaskets you need to do the job, where to find them, and the difference in cost from OEM. Of course, OEM is always a great way to proceed, but carefully-chosen aftermarket parts sources can save you $$. K & L is a good gasket supplier.
Carb enricheners out of adjustment:
Jet block and the brass fuel jets inside:
K & L carb kit, left, enrichener gasket; right, jet block gasket. brass round sleeve is the float needle seat, silver piece is the float needle valve. The float bowl gasket is the big oddly-shaped one, and the O-rings fit various points. The little one, when you remove the CV carb diaphragm caps, is at the 6 o'clock position on the carb body, beneath the CV carb diaphragm cap. Sometimes it stays on the carb body, sometimes it stays on the cap, sometimes it falls-off and hides from you immediately.
Splitting the carbs into two pairs as-showm allows you access to remove the float bowls to remove the jet block, and to access the pilot jet and the main bleed pipe.
The red line shows the O-ring I mentioned above (the K & L description), where it's supposed to be, until it falls-off and hides somewhere.
These get tightened until the L-shaped piece bottoms out on the clamp base. Snug is fine, they don't need to be over tightened. If they aren't tight, you can have a vacuum leak. The airbox to carburetor airhorns rubber 'donuts' and the bottom of the carburetor to VBoost manifold rubber 'donuts' can develop leaks if not tightened sufficiently. They get surface cracks with aging, but still are sealed, in many cases. The way to check for leaks is to spray them with starting fluid and see if suddenly the RPM's rise, indicating you've sprayed a leak. Continue spraying there may be more-than one! Be aware there is a thin rubber O-ring on the base of the VBoost metal manifold where it fastens to the cyl head. These are known to leak, use the same spraying procedure. If you find one is bad, replace all-four.
A word of caution, I don't suggest working on a bike's fuel system in your garage if you share the space with a gas hot water heater. Gas vapors can travel 30+ feet to a source of ignition like a gas hot water heater!
Taking pictures as you do a tear-down helps to allow a proper re-assembly.
The shop manual is your VMax Bible. There are a few errors in there. Yes, there's a thread on that, too, use the search engine to find the thread.
Between the factory shop manual and the search function, you can answer almost any question you may have.