Newbie alert! Some new gardener questions!

Hello all. Me and my hubby have just bought a new home with a lovely garden. After 8 years in an apartment, it's all very exciting :-)
So, my questions and hopefully someone can provide some advice:
The house was empty for c6 weeks so my main priority at the moment is weeding - loads of that tall one that goes purple which is coming up easy. The difficult part is grass and moss in the borders. I'm currently pulling up the grass and as much moss as poss then turning the soil with a fork. Am I doing the right thing?! Struggling to get all the moss so am turning. Was thinking of adding some compost (as have an established compost with lots of worms in) - is that a good or bad idea?!
Secondly I'd like a hedge at the front of the house. Specifically fast growing evergreen. Any thoughts?
Lastly we also have a couple of houses where their gardens back on to ours. The fence is small... I've counted we'd need 20 panels just to do one side so out of budget at the moment. Any big shrub/bush recommendations? We've already got quite a bit of laurel, holly and conifer so something else

Many thanks and sorry for the ramblings!

 

Thank you John! That's good news re the moss. I started trying to scrape it all off which was taking yonks! I'll check out those shrub/bush recommendations, thanks!
The front hedge is because front is in a road so to block out traffic noise and for privacy and security :-)
Thanks again, really appreciate your response

 

Ooh loving the red robin!!!

 

Hello @Mrs C , to the forum.
Many congratulations on the new house, I wish you every happiness in your new home

 

Thanks so much Beckie :-)

 

Thanks Armandii! I shall take some pics today and add with some descriptions :-)

 

Has that worked?! Ok first is back garden. Strange shape, concrete wall isn't too pretty but at least it's tall so private that side. Bushes are in slightly strange places at the moment. We're south facing and the soil seems ok! But stony but not bad. Some worms etc. This is the front so rockery by the drive. That's a road behind the wall hence me thinking a hedge along

 

The grass has scorched slightly from non proper distribution of weed and feed plus us not knowing the mower wheels could be lifted. We now know and have bought a spreader :-)

 

This is the west facing side (if west is morning sun) - quite a few bushes here including rhododendron holly and laurel

 

Welcome to the forum! Lovely pictures that you've shared too!

 

Finally patio and bed at the other side
Ooh missed a pic I thought I'd posted! Thanks John, I hope so. Just need to decide what to do! I've been told I need to wait a year to see what's already planted :-)
Thank you Lori
Looking forwards to chatting on here and getting advice