Well...without knowing what your specific requirements are for a personal account, it is hard to give a definitive recommendation. However, if you are looking for ease of transfer, good customer service and a bank that is solid (ie. larger offshore bank), I actually would encourage you to consider Mauritius Commercial Bank (MCB). You don't hear too much about them, but they have been around forever, I really enjoy dealing with them, and their customer service is good. They also are very socially conscious, occasionally donating funds on your behalf (not your funds from your account) to various local charities. They have internet and mobile interfaces, though if you are applying, talk with me first, as getting the internet access is not as straight forward...and it does require a small purchase of a security token. You want to do all this during your application process.
There are many other banks out there that are good, but in general if you are looking for a bank that is solid, that you can open a personal account remotely, the customer support is good, and the transfers are fast (and fees are very reasonable), you may wish to consider MCB. Oh, one thing - personal accounts are denominated in the Mauritian Rupee (MUR) so bear that in mind. I don't believe there are any minimum balances as far as I am aware.
Of course, there are other factors, depending on where you are located. If you are a US citizen/resident, your options are a bit more limited. Also, some banks that are open to Europeans and Asians, may not be open to North Americans. Some banks have visitation requirements, while others have limitations on transfers, etc. (ie. if you have a bank account in Iceland, there are currency restrictions in moving money back out).
Of course, Euro Pacific Bank is very much worth consideration for just a basic account - it is advertised here. No interest bearing account though and a fee that is like 5.00 US or something like that per month. Americans are not accepted. Transfers are a bit on the pricy side. But transfers in and out are good. So basically EPB is more to just park some cash.
Again, much depends on your expectations, how much money you want to put in, your tolerance of fee structures, etc.