I'd have thought that Southampton, Bournemouth and Weymouth would demand more paths than Salisbury/Exeter (bearing in mind Exeter has an alternative faster route).
Some of the above 16 services passing through Basingstoke will need to call additionally at Farnborough Main, as at present the 4 services that call there struggle to cope with passenger numbers during the peaks. To put this in perspective it has about 1/2 the passenger numbers of Woking and Basingstoke but doesn't have the same level of direct services, so it is likely that it would need a little more than 25% of the services that Basingstoke will have.
Basically I took the current service and doubled it.
There are currently two per hour to Bournemouth plus a stopper that calls at All stations south of Woking. In my scenario those are upped to four per hour all terminating at Basingstoke. Two of them could easily be extended onto Southampton giving six per hour to Southampton
4 per hour to Exeter is never likely to be needed but 2 to Exeter and 2 to Salisbury is not beyond the pale. (or even 1 to Exeter, 1 to Salisbury and 2x peak onlys to Andover post electrification)
For Farnborough, if you put fast to slow links in south of Pirbright, some or all of the 4 per hour peak onlys to Woking/Basingstoke could cross to the Slow lines there and call at Farnborough and Fleet.
I'm also going to rebuild Micheldever so that the current island platform becomes two terminating bays, move the up platform at Micheldever back to its original alignment and build a new down main and platform on the east side of the Island platform. This is because operationally this removes the conflicts that terminating trains at Basingstoke would cause.
So including your comments.
Crossrail
Four Per Hour Twickenham via Kingston
Four Per Hour Shepperton via Kingston
Four Per Hour Hampton Court
Four Per Hour Chessington South
Four Per Hour Dorking via Epsom
Four Per Hour Guildford via Epsom and Effingham
Slow Lines
Four Per Hour Vaux, Clapham Jct, Wimbledon, Raynes Park, Surbiton Hinchley wood and all stns to Guildford
Four Per Hour Vaux, Clapham Jct, Earlsfield, Wimbledon, Raynes Park, Surbiton, Esher and all stns to Guildford via Woking
Two Per Hour Vaux, Clapham Jct, Wimbledon, Raynes Park, Surbiton, Walton, Weybridge, Woking and all stns to Alton
Two per hour Vaux, Clapham Jct, Wimbledon, Raynes Park, Surbiton, Walton, Weybridge, Woking and all stns to Micheldever.
Four per Hour Vaux, Clapham Jct, Wimbledon, Raynes Park, Surbiton Thanes Ditton, Hampton Court (peak only)
Fast Lines
4 Per Hour to Poole (2 onto Weymouth)
4 per Hour to Salisbury (2 onto Exeter)
4 Per Hour to Portsmouth via Guildford
4 Per Hour to Woking, Farnborough, Fleet, Basingstoke, Micheldever only (Peak only) (Cross to slow at Farnborough)
2 Per Hour Woking and all stations to Alton (cross to Slow at Woking)
2 Per Hour Woking, Farnborough and all stations to Southampton (cross to Slow at Farnborough)
2 per hour Woking and Guildford only (peak only)
2 per hour Portsmouth via Eastleigh