The Kingsclere route is good but it’s a fair bit of road riding to get there if you don’t want to drive.
If you want to ride from Aldermaston then I’d recommend –
Get on the canal at Aldermaston and follow the towpath towards Theale, from Theale take the footbridge over the M4 then there’s a bridleway that will take you up to Sulham Wood. There’s some small trails in Sulham Wood to play on, a few steep short downhill bits to mess around on and a few jumps if that’s your kind of thing.
From Sulham you can head towards Pangbourne and join the thames path at Whitchurch Hill which is surprisingly good to ride if you head towards Goring (just watch out for the steps as they’re notorious for bike accidents). If you leave the thames path before you reach Goring there are loads of bridleways that take you up towards Woodcote and Checkendon where there’s loads to explore.