I think it would be very helpful to have a price and time limit in the search engine. Say you have a budget and you really don't want to search through pages of overpriced pets, or you're in a hurry to find the right pet but you don't want to pay the buyout price to get it fast.

I am very aware that there are arrows above the level, starting bid, current bid, etc. to sort by that particular variable, but right now you can't select multiple ones at once. This would be very difficult anyway, because the system would need to compromise between the two variables.

If there were limits on current bids/starting bid/buyout/time left (not necessarily all, but at least a couple) in the search engine, you could be specific. Any pet that's over your budget won't be listed. Any pet with a longer time remaining than you want won't show up. This would be extremely convenient because you could choose more than one variable at once, so you don't need to click the arrow on one and scroll through pages to look and see whether the other variable is reasonable or not for a particular pet.

Commenting with any support/extra recommendations/potential problems would be very helpful!

You can click on the table at the top of the auction and sort by the autobuy, timeout and so forth. I think it would be neat to search them because then you could narrow it down to two catergories at least. 

I normally sort by the price and don't scroll down past my budget, or if I want a quick pet I sort by the auction time and end when I feel like it.

Just a thought ^^

 I like it

I was going to suggest something similar, because I might see something I need/want and the price is over what I have. It irritates me that I cannot put in a price range on items that I might be looking for.