You can take three general approaches to this:

• If you simply want to get this done so you can move on to other things, acquire a <a href="/wiki/Partisan_Messenger_Tortoise" title="Partisan Messenger Tortoise">Partisan Messenger Tortoise</a>, <a href="/wiki/Hound_of_Heaven" title="Hound of Heaven">Hound of Heaven</a>, and (if you can) <a href="/wiki/Viric_Lizard" title="Viric Lizard">Viric Lizard</a>. Play whatever you end up with and <a href="/wiki/The_Airs_of_London" title="The Airs of London">cycle Airs</a> if none of your options are available.
• If you are an inveterate optimizer who wants to make absolutely maximum use of your actions, use only the <a href="/wiki/Viric_Lizard" title="Viric Lizard">Viric Lizard</a> option (and/or somehow convince someone to send you a <a href="/wiki/Mycological_Bullfrog" title="Mycological Bullfrog">Mycological Bullfrog</a> at Whitsun) and <a href="/wiki/The_Airs_of_London" title="The Airs of London">cycle Airs</a> if the option to study the Lizard doesn’t show up. This will most likely require repeatedly ducking out of and back into the lab, but such is the price of optimization.
• If you are lucky enough to be on a <a href="/wiki/Whitsun_(Guide)" title="Whitsun (Guide)">Whitsun year</a> with <a href="/wiki/Scarlet_Egg" class="mw-redirect" title="Scarlet Egg">Scarlet Eggs</a> available, you can also acquire the <a href="/wiki/Amber_Iguana" title="Amber Iguana">Amber Iguana</a>, <a href="/wiki/Warm-hearted_Amber_Iguana" title="Warm-hearted Amber Iguana">Warm-hearted Amber Iguana</a>, and (with an <a href="/wiki/Highly_Illegal_Experimental_Augmentation_Device_(Probably)" title="Highly Illegal Experimental Augmentation Device (Probably)">augment device</a>) <a href="/wiki/Rubbery_Dragon" title="Rubbery Dragon">Rubbery Dragon</a>. Your research will be a bit slower, but you'll pick up lots of <a href="/wiki/Shapeling_Arts" title="Shapeling Arts">Shapeling Arts</a> along the way. However, if Whitsun is nowhere near, don't bother waiting more than a few months: <a href="/wiki/A_Complete_Account_of_Frogs,_Toads,_and_Other_Croaking_Beasts" title="A Complete Account of Frogs, Toads, and Other Croaking Beasts">the result of your research</a> is just too useful in lategame money-making.

The <a href="/wiki/Ocular_Toadbeast" title="Ocular Toadbeast">Ocular Toadbeast</a> is insufferably difficult to acquire, requiring an entire <a href="/wiki/Flute_Street" title="Flute Street">Flute Street</a> carousel and <a href="/wiki/The_Formula_for_Empyrean_Redolence" title="The Formula for Empyrean Redolence">Empyrean Redolence</a>, and thus is absolutely not worth going out of your way for.