I find I want to do it when traveling. The question I have is....
The first question should be, why, when going to a location you've never been to, you immediately want to plan to ditch the "group" and take off on our own?
I can only speak for myself, but when I travel to a new location, I always stick with the "group" for at least the first dive or 2, pick up the local knowledge, etc. Especially if you will be diving with the same dive operation. That also gives the operation a chance to judge your abilities too.
Couple of examples, I went to Jamaica, went out with the dive operation, for the first dive, took one look at the reef, put away my gear and snorkeled the rest of the time.
Went to Hawaii, first dives were off Oahu, it was ok, as I left the DM asked if I was coming back, I was honest and said, it was fun, but nothing different than S Florida, with that he took me aside and told me they were going to the North Shore later in the week, I should go. And I did, awesome diving and by the second dive they openly told me to take off on my own and see things they would not allow the group to see. By the second day that had me DM'ing one of the dives! It was great. Point is, had I just "taken off" on my own early on, I would have never had the later opportunities nor would I have built the trust with the operator.
As to your question, again, that goes back to location, will you even need any "solo" gear? Not if your diving a 30' reef for the whole week. And if it will be more advance, just call the operators you are considering and see what gear they offer. That is really the answer to your question.