Apart from starting with the cheapest silver and all the rest, more to your question on looking for premium coins...
The best advise I can give you is to know the best prices in your country/city/area and look out for bargains on any/all bullion coins. Kookaburras, Koalas, Pandas are al higher premium coins, but as they are more collectable due to different designs each year, their value seems to go up with time. There are also key dates that you should look out for e.g. 2015 Panda was the last 1oz Panda (2016 onward only 30g), and not marked with content, fineness or weight.
I like to collect series coins like the Queen's Beasts, Creatures of the North, Australia's Most Dangerous, Myths and Legends and many more. If you get a good price on these collections, you should at least make a bit of money over time, if not making a nice profit selling to another collector.
Do not sell your bullion to a coin shop if they only pay spot. CRAZY! Get on forums like this, or local buy and sell trading platforms where you can buy and sell from like minded stackers and collectors. I have never sold a coin for less than what I paid.
Watch out for crazy prices on Silver Eagles - they might be big in the US but here they are expensive, and you don't get your money back on them.