Change songs sequence in iTunes playlist is now easy in newer version on iTunes 11, 12 or later. here I gave complete guide on how to reorder songs in Playlist. There is no option for move directly in list. So any time you can play your favorite songs at first from playlist. Not only on iTunes but you can also manage playlist on your iOS device (iPhone, iPad and iPod Touch) by Edit, Remove, Rearrange songs inside playlist by drag song.
If you want create new or Edit playlist in iPhone music App.
Note: here I explain on Mac’s iTunes but same steps are applicable also on Windows iTunes.
Steps on how to reorder songs in Playlist From iTunes: Mac, Windows PC
Step 1: Open iTunes on Your Mac/ PC. (From the Spotlight Search type iTunes and open).
Step 2: From the top iTune’s tab, Go with Playlist. 
Step 3: Open Playlist by tap on name,
Step 4: Now, Choose song that you want move anywhere in playlist. See the below screen, there I moved first song inside the playlist.
In your case if you can’t able to choose/ Select song from playlist and drag anywhere in list then share with us.
This changes automatically applied when your iPhone Sync to your Mac or PC’s iTunes. But mind that you can easily rearrange or reorder song in created playlist from iOS device’s music app easily. For that you don’t have to need iTunes on Mac or PC.
in the case for shorting songs with different types you can easily do with short by option. See below screen. Name, Gener, Year, Artist, Album and Time. 
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