I think you need to ask yourself why you want a 1x drivetrain. What is that going to do for you that your current system does not?
Presumably you want more rear derailleur gears than your current 8 (why would you want an upgrade otherwise?) That means you will have to get new shifters as well as rear derailleur, cassette and chainring. You can run a single ring on a double crank but you'll end up cross-chaining on either your highest or lowest gears, so a new crank is advisable.
It's likely that the cost of all that, plus having a shop install it for you or buying the special tools required if you do it yourself can be significant compared to the purchase price of the bike.
If you really want to do it you have a few choices:
Lower level of dedicated 1x11 system such as SRAM Apex 1. Obviously the best but most costly option. Note, this option may also require a new rear wheel in addition to the items listed above as 11 speed road cassettes generally need 11 speed compatible freehub bodies.
9 or 10 speed mountain derailleur with a 9 or 10 speed road right hand shifter. I believe Shimano mountain and road systems used the same cable pull ratio up to 9 speed. SRAM mountain and road systems use the same pull ratio throughout (at least for older systems).
Road 9 or 10 speed rear derailleur and right hand shifter, use a derailleur hanger extension to enable running a larger range cassette. (Road derailleurs usually support a 28, 30 or sometimes 32 tooth max sprocket. You will probably want 34 or larger.) This is a bit of a hack but ensures compatibility between derailleur and shifter at 10 speed. See this recent GCN Tech video for info on this method.
By the way, for road riding you will not need a clutch derailleur as the chain will not be bounced around. You could use a narrow-wide chainring for better chain retention, or just leave the front derailleur in place to keep the chain on the front ring.