You may want to get a professional in to spray as they have access to stronger chemicals BUT you will then have to wait for these to dissipate from the soil before you can plant.

Only effective way to dispose of the saplings is to dig them out - if that's not possible, then saw them down to the base and poison the stumps with SBK, tipped in a hole drilled in the centre. Alternatively, you could hire a tree stump grinder for use once you've chopped the trunks down (don't know how big the trunks are though, only effective on largeish stumps) or call in a professional tree surgeon to remove the lot, including stumps and roots.

I would suggest going over the whole garden with a strimmer/brush cutter to get some control and the start digging beds out.

If this was once an established garden, there will probably be many interesting and valuable plants, shrubs and trees still growing here amongst all the weeds and undergrowth.
Before you do anything drastic, and I'd suggest this is not the right time of year for such major work, check carefully around to see what is coming up in June and July. There may be many plants you can mark and put temporarily into pots in the autumn including shrub and tree seedlings you might want to use.
The best time to do the clearance would be in the autumn as this will have less impact on the wildlife. Doing it now at the height of the breeding season for birds, insects, mammals and reptiles like slow worms, frogs, toads etc would be an environmental catastrophe. In the autumn most will be able to escape the work.

Bertie - an extremely good point!