The cheapest and best upgrade would be to add Bilstein B8 dampers to the H&R springs. I would get MK6 ones as they're more forgiving.
Coilovers are a blue pill vs red pill thing. A rabbit hole you don't want to go down unless you have specific requirements!
I can honestly say coilovers are the most over rated bags of sh1t I've ever experienced on a road car. Even expensive ones. The best ones I've used are Ohlins but you'll be coughing up £2.5K for them, they'll last 30,000KM (yes, KM, not miles) and you will get ZERO support if they fail, which they WILL. But for the short window they last, they are utterly sublime. As for cheap £300 JOMs and the like, I wouldn't fit those to a scooter let alone a car.
EDIT: GVK beat me to it. Most coilovers are, at minimum, twice factory spring rate (they have to be due to the lowered roll center) so ride comfort will be terrible.....except....where the dampers are rebound/compression adjustable and top quality tuned to the spring rate and vehicle axle weights. Cheap ones aren't. A lot of suspension makers just chop the springs down an arbitary amount without actual on-car testing. That's why I went with Ohlins because they do 6 months road testing before releasing to the public, but even that level of diligence doesn't gaurantee a reasonable life span
See, I did say red pill...... just take the blue pill (B8s) for an easy life.