Welcome to the forum and the madnes that is Vulcan, David. Congrats on the new ride, you are going to love it, even though th vn has a few issues, as do most bikes, as I am learning.
The electrical charging system is marginal. If you had to boost the battery last night before the ride home, it did not get fully charged by the bikes electrical system. Many riders keep their bikes on a battery tender overnight. The battery is mainly for starting the bike, and the charging system for keeping it running once started. If you rely on the charging system to recharge a depleted battery, it is hard on the stator and regulator-rectifier, and will lead to premature failure. You want to avoid this, as it virtually requires pulling the engine to remove the left side cover to change out the stator.
I hope the new battery you ordered is a Maintenance Free- Absorbed Glass Mat (MF-AGM) type, and not an ordinary Lead Acid type. If not, try to contact the supplier and see if you can change the order before they ship it. Go to the verses and the electrical forum for much more info about this.
Changing to NGK iridium spark plugs has also made a big difference in ease of starting and better running, many members report. You want NGK DPR7EIX-9 Iridium. They are pricey, or a bit dear, as you Brits say, but worth it. (I am asuming you are a Brit from the reference of 750 pounds price of your bike).
You can make a set of motorcycle jumper cables quite economically with an 8 to 10 foot long piece of 14 or 16 gauge 2 conductor lamp cord or extension cord wire, 2 sets of medium sized battery charger clamps and 4 pieces of heat shrink tubing. OK, the UK has 220 volt and your cords are heavier, so use 2 pieces of automotive primary wiring, in the same gauges as above.
Make sure you slide the heat shrink tubing on the wire before attaching the clamps, and get both black clamps on opposite ends of the same wire. Then the same for red clamps. Using several more pieces of the shrink tubing every 6 inches or so, around both wires will keep them together and neater. The set I made took 30-40 minutes and weighs about a pound. It will roll up small enough to fit in a side jacket pocket or the sissy bar toolbox.
We can tackle the tach issue after you get the bike running, and see if it is still a problem.
While waiting for the battery, go over the whole bike, checking that all nuts and bolts are tight. All electrical connectors are clean and packed with DIELECTRIC GREASE. All grounds (earth wires, to you, I believe) are clean and tight.
We recommend using Seafom fuel additive here in N. America, but it is not available in the UK. Find something similar available to you, and use it as required.
As mentioned before, spend a little time in the Verses and the various forums for many ideas on things do or watch for.
I almost forgot the rear splines. If you do not have a maintenance log book from the previous owner and do not know if the splines were greased when the last new rear tire was installed, you will want to do it in the near future. You might want to change all your fluids, so you know what you have. Now I have to apologise for my long post... I hope you are up and riding again soon. Hoss