Getting to lulworth past three areas of overfalls, time it takes will depend on your rib and engine package, your experience and what the weather is doing, on a good weather day it wont take that long at all and the scenery is spectacular along the way. You can hug the coast in good weather getting close to the cliffs if you know the area well enougth and check your charts.
Lots of nice bays etc to explore. My favourite is Warbarrow Bay, on a nice summers day Studland Bay will be packed and so will lulworth cove, but Warbarrow Bay is always nice and quite. If the army ranges are open you wont be able to get to lulworth but times and days are advertised, if it is firing day you can still go round to Chapmans Pool which agin is a nice quiet spot but if overfalls running high and your uncertain of taking the inside dash through them which runs extremely close to the cliffs then not advisable.
I would recomend Cobbs Quay as a good base, if you join as its an MDL marina then lots of benefits. If you have a biggish engine or use your rib a lot then taking advantage of the fuel at discount which you get with MDL can save significant amounts especially compared to Fuel costs at somewhere like Salterns marina or the fuel barge in the harbour. Plus at Cobbs you have showers, cafe and all other amnenities.
If considering being based from Poole go visit some of the marinas etc and have a chat with the staff. Also would recomend if intending to cruise in this area buy a book called "Inshore Along The Dorset Coast" by Peter Bruce, excellent book giving lots of information about the Dorset area and hazards etc.
Poole is a great base as youve got many great areas not far away like the Solent, Dorset Coastline, Isle of Wight etc to explore and on really crappy days with bad weather if you still want to go out you can explore Poole Harbour itself.
As to the two bridges to navigate to and from Cobbs Quay, I have a 7.5M rib with an A frame and have always managed to go straight under both, only pain Ive had with the two bridges has been on very busy summer days with the amount of muppet heads waiting for them to open and being very inconsiderate and blocking the channels with their gin palaces due to poor boat control, that can be a bit stressful at times.