Toll will be about 29 euros.
When entering the highway from Gorizia the first toll station is "Villesse". Then you travel towards Venezia Mestre, Padova, Bologna and then Rimini.
Exiting from "Rimini nord" (northern Rimini): 28.30 €
Exiting from "Rimini sud" (southern Rimini): 28.90 €
To calculate prices check this site:
"Partenza" is the entrance in the highway, "Destinazione" is the exit.
Also viamichelin.it gives you an estimate of prices. Highway and vignette prices are usually correct. (be careful as it sometimes suggests an itinerary out of the highway).
In Italy tolls are calculated on distance. You have to take a ticket from the machines when entering the highway. Keep the ticket and show it when exiting.
Some highways or part of them are free of charge (Trieste's "Fernetti" border to toll station "Trieste Lisert", which basically is Monfalcone; Gorizia to Villesse).
Some more suggestions for your trip:
Stop at a petrol station in Slovenia before entering Italy, petrol is much cheaper.
I don't know your travel plan, but I would suggest crossing the border towards Trieste (border Sežana/Fernetti). "Trieste Lisert" - "Rimini nord" costs 29 € and is faster as you practically never get out of the highway. Between Nova Goriza (Slovenia), Gorizia (Italy) and then the highway, you travel on regular roads.
In general you can pay using a Credit Card on toll stations that show this sign:
Queues are generally shorter/faster. =)