You'll find more about the voucher in the Ultimate Guide sticky. But basically it only works for a miles-only booking. You still have to pay fuel surcharges and taxes (on both tickets) so you won't get much value booking economy.
You can Book WT+ and upgrade but this can't be combined with the voucher. WT+ would be at least £600 I guess, so now you have the voucher you're better off making use of it. The good news is that NYC is business class is going to drop to 80k in a month's time - you could just buy 24k miles or £399 and you're basically there.
The sweet spot is really earning a voucher and >100k miles per year. Most of us who don't fly a lot bridge the gap through Tesco or some other partner. At the moment, getting a Amex platinum card would be a good option if you qualify (£40k household income). For the £300 fee you get 42k miles, travel insurance and other benefits. You could also refer your other half and get 22k+42k for £300 which gets you started for next year's voucher! Let me know if you want a referral.
If you go this way, you're nearly at 100k which after the Avios change is enough to go out in First and return business. I think it's well worth the stretch.