foomar's answer is a good one, forking and digging by hand is by far the best - if hardest method.
think what you want to do with the land - dont be overwhelmed - take it a square at a time. any you want to cultivate can be dug or laid over with a membrane of some kind for future digging. any you want to lay to rough grass can be regularly mowed and the grass will win over the weeds.
as for roundup, it's admirable that you dont want to use it, but over the years i have learned that sometimes, used judiciously and sparingly, it can be a good thing - indeed it can increase biodiversity. for example if you have a hedge or shrub overgrown with bindweed (Calystegia sepium) - digging it out is not an option without digging out the whole hedge. you could hand-pull it regularly for a few years but this is pretty impractical. cut the bottom of a flowerpot or box, gather the offending vegetation into it and spray so the plant gets all the spray (rather than the soil) this kind of spot treatment can really help. alternatively mic it with wallpaper paste and paint it on.
but most importantly come of with an overall plant for what you want to do - then execute it. this may take years but when it is finished it will all come together.
good luck
VG
think what you want to do with the land - dont be overwhelmed - take it a square at a time. any you want to cultivate can be dug or laid over with a membrane of some kind for future digging. any you want to lay to rough grass can be regularly mowed and the grass will win over the weeds.
as for roundup, it's admirable that you dont want to use it, but over the years i have learned that sometimes, used judiciously and sparingly, it can be a good thing - indeed it can increase biodiversity. for example if you have a hedge or shrub overgrown with bindweed (Calystegia sepium) - digging it out is not an option without digging out the whole hedge. you could hand-pull it regularly for a few years but this is pretty impractical. cut the bottom of a flowerpot or box, gather the offending vegetation into it and spray so the plant gets all the spray (rather than the soil) this kind of spot treatment can really help. alternatively mic it with wallpaper paste and paint it on.
but most importantly come of with an overall plant for what you want to do - then execute it. this may take years but when it is finished it will all come together.
good luck
VG