The usual way most people do it is to make up the system voltage with batteries in series first and then parallel each series set until the bank is complete. i.e. in your case the second option you have described. [series/parallel]
However, there is an advantage in making two parallel sets and then putting those in series to make up your system voltage. When done this way the batteries seem to balance better. They do this mainly due to the fact that all batteries will always be at the same voltage in each parallel set, I suspect. I have done this with a 24 volt bank (made from placing two paralleled sets of 12 volt batteries in series) and it works great. I don't see any reason why it wouldn't benefit six volt batteries in the same way. Bear in mind it takes slightly more interconnects to do it like this, but only a couple more. [parallel/series]
There is a third way which tries to gain the advantages of both methods. The H bridge (yeah, similar to what's inside an inverter). You wire your batteries in series/parallel, just like the typical way. But then you join the mid points of each series pair together. Imagine if this was done with just four batteries, it would look like an "H". If done with six, eight or more it starts to resemble a "ladder". The whole point of this is to keep the basic layout like the series/parallel option but obtain the balancing advantage of the parallel/series option.
I have tried all three ways with my 24 volt bank & personally I prefer the parallel series method. The H bridge arrangement worked pretty well, but it is all to easy for "lazy" batteries to hide within the pack and harder to rat them out!
If you do happen to embark on a parallel/series scheme, it would probably work out best to put two older batteries and two newer batteries in each parallel set.
As it happens the last time I was really active on this forum was when I was deciding about all of this with my 24 volt bank! lol