Train travel around europe help required

Ok i have booked accomodation and flights on my first leg of my europe tour i fly with easyjet from Gatwick ( i am a 36 yr old male first time traveller like this before) on the 14th of May to Amsterdam stay for 4 nights at Bulldog hostel.
Then fly easyjet to Basel on the 18th stay 2 nights
Train down to from Basel to Lauterbrunnen and stay 4 nights
Train from Lauterbrunnen to Innsbruck and stay 4 nights
Train from Innsbruck to Venice stay 2 nights
Train from Venice to Florence stay 4 nights
Train from Florence to Rome stay 4 nights

So as you can see i will be making 5 train journeys in the main plus maybe a few journeys whilst in Lauterbrunnen and Florence to neighbouring towns.

As i see it i can buy a interrail pass for either 22 days at a cost of £431 or 1 month at £550 so as the main journeys i have costed point to point tickets at around £240 plus a few other journeys won't come close to £431.
I have looked at a swiss pass for the 2 train journeys but even this wont really sae me any money so i figure point to point tickets are my best option.

My question is can i purchase a ticket in basel to take me to Innsbruck via Lauterbrunnen bearing in mind i will be staying there for 4 nights, and the same applies to me travel in Italy.

As i am a first time traveller if anyone can give me any precious information on backpacking in general or staying in these destinations it would be most appreciated.Thanks

Train from Innsbruck to Venice stay 2 nights
Train from Venice to Florence stay 4 nights
Train from Florence to Rome stay 4 nights

Tip: Buy a train ticket Fortezza-Rome via Venice and Florence in Innsbruck. It will be cheaper than buying Venice-Florence and Florence-Rome in Italy. The sales person at the ticket booth in Innsbruck will ask you for the exact connections because usually you reserve trains in Italy. If you want it very cheap refuse to do so and tell them you want regional trains only, no reservation. It will get you the cheapest possible ticket for travelling around Italy. You'll also need another ticket from Innsbruck to Fortezza, get this in Innsbruck too.

Once on the European mainland (as opposed to the UK and Ireland), you can get a ticket from anywhere to just about everywhere else. It is nearly always the case that local trains, although they take longer and involve numerous changes, will always be so much cheaper than international ones. My suggestion would be to just arrive, look at your map, go across one country on the national service - then change on to the next country's trains as close to the border as possible.