There are a number of physical formats you can consider when buying platinum:
As a general rule, you should look at buying legal tender platinum coins wherever possible. This will almost certainly include less overhead and premium than other formats, and be closer to the true spot price of platinum.
Purchasing rare platinum coins should be avoided unless you really know what you're doing. Some subjective measures of value are easy to misjudge, and may result in you getting taken advantage of.
Buying platinum on credit or speculating on the future price can lead to getting yourself in a significant financial jam.
Instead, put some money to the side that you're sure you're not going to need in a short time horizon, and use that to invest.
Platinum owned through a commodities exchange, or "on paper" is no substitute for physical bars, coins, or jewelry. Exchanges are heavily leveraged, which means if everyone tried to "cash out" at once, there isn't enough physical metal to go around.
Moreover, precious metals are typically meant as a hedge against the complete collapse of the traditional banking infrastructure. If you wind up needing it, you'll want to have it close at hand!
Physical precious metals like platinum are a hedge to the traditional banking system. In a crisis, if the system collapses, it may very well take your property down with it (if it can).
If there is a run on the banks, having your platinum under your direct control means they can't confiscate it, block access to it, or have loaned it out in a leveraged fashion.