Hi Nick,
I don't do any sea fishing myself but I know that it can be quite good. My mate Bill has caught big bass from the beach in the past. They do boat trips from Poole harbour which isn't too far away from the forest. It is quite nice on the quay and the boats go from there so they should be able to give you the info. Sorry I can't be of more help but I don't go sea fishing.
Regarding day ticket waters I may be able to make a few suggestions as there asre several in the forest. It all depends on what you want. Sway lake would be my first choice. It gets pretty busy but there are loads of 2lb roach, big perch and carp to over 30lb. You buy the ticket on the bank. Night fishing is allowed if you fancy this but you can catch the roach in the day and there are plenty of them. If you want a commercoial carp fishery Hordle lakes, near New Milton, are worth a look. Again you get the ticket on the bank. There are carp in all of the lakes but the big lake is probably best for bigger ones. There are also some decent roach and a few big perch there.
There are lots of other day ticket waters and it may be worth your while popping into Ringwood Tackle and having a chat with Ritchie. The phone number is 01425 475155. He should be able to give you all the information you need.
I hope this helps and that you have an enjoyable weekend.
Dave