The 3 most popular ways to sort are:
1. Hit Creation Date - Newest First
The benefit for this sort is 2 fold. Some requesters will post a few hits at a time but will continue posting hits for hours or all day, depending on the requester. Some do this simply to stay on top of this search page and others do it as they have work available via some sort of automated system. If you happen to work for one of these requesters you might only get a few hits in before there is no new hits available. However, if you complete a hit and save that page as your favorite bookmark page, when you open it up again you'll automatically accept a hit when you go to the bookmark if it's available. This all said, when you submit a hit and no more hits are available, if you continue to refresh that page, if a hit becomes available you'll auotmatically get accepted.
Of course this works with any search listing. But there is zero reason to refresh other search pages frequently because they just don't change as much. Refreshing the newest hits first will also give you a jump on your other favorite requesters as soon as they post (you'll see the post but not accept it if it wasn't the last hit you submitted and didn't change pages) and you'll also get first dibs on more lucrative hits that might have a small amount of work available like higher paying surveys or other popular high paying hits.
2. Hits Available - Most First
This is a popular way to sort lower paying quantity hits. Lower reward amount, not lower dollar per hour hits. If you can do a $.02 hit in 10 seconds you can make close to minimum wage and if the requester has 10,000 of them available, you can make some easy money if they are hits you enjoy doing, do them well, and do them fast. Some requesters will post tiny batches to stay on top of hit creation page and some requesters will post batches of thousands at a time.
Doing these types of hits isn't guaranteed to be a money maker. Most of them aren't. There are plenty of requesters that want to pay a penny for 10 minutes worth of work. However viewing the ratings on TO and trying the hits yourself you'll soon find out which ones are worth doing. And if you find those hits you might be able to do them for several hours, though there are some very popular hits that 10,000 hits can be gone in minutes.
3. Reward Amount - Highest First
This is typically not a popular way to sort generally. You'll see a lot of spam hits that break the terms of service. A lot of them will have fake submit buttons so you can't even submit them and others will just reject them if you do submit them. They are under no obligation to actually pay. The biggest problem with these types of hits is that they might ask for personal information you shouldn't be giving out and may even ask for credit card information (credit card fraud), cell phone number (charge calls to your cellphone) and email and snail mail address (sell your information to spammers).
So when search this way? When you are searching by a keyword or a requesters name. For example, if I decide to search for surveys I'll sort this way, filter out the scammers and spammers and see if there are any legit (.edu type) surveys that pay decently enough to do. I don't recommend surveys though since amazon doesn't explain to requesters how bad blocks hurt workers so unknown survey requesters could put your account in jeopardy, amazon won't help workers, all because they wanted to prevent you from doing the survey more than once.
Most typically you sort this way when searching your favorite requester that posts multiple hits. For example, you might do transcription and you want to get the highest paying hits for your favorite transcription requester. Less commonly, I might even search for lowest reward with my favorite requester for this same reason. The grading hits are typically at the bottom of the pay scale for requesters so search this way might show you these types of hits up front, if it's something you want to do.