Good quote, ylblai2. This is why my training doesn't include blitz. But occasional blitz games with my arch nemesis for fun...
4 hours a week to get better - what should I do?

Time Saving Tips for the Chess Player Who is Too Busy to Study
You can take some advice from an experienced IM and FIDE trainer(click here to see it).

Do at least an hour of tactics trainer a day (if you have the time!). Also, try to complete a few endgame drills per week. Practice makes perfect! Also, play a little Daily Chess and use Analysis during your move. Then Computer Analysis at the end of your games to see where you went wrong. Also, play a little Blitz here and there to see how you're improving. Finally, enter a tournament or two near the end of your 25 weeks to test your new skills.
Here's a cool puzzle. If you don't want to do it, that's OK. It's completely optional.



There's a empirical rule that to become expert at a demanding activity requires about 10,000 hours of focussed effort (let's forget about natural talent, which is difficult to do without entirely). So in 4 hours a week over 25 weeks, you can aim to become 1% expert. Which might be above average.
IM Yaacovn is right. Devote over half your playing time to slow play if you want to improve. Turn-based chess is probably more useful once you are able to analyse a bit further ahead. Blitz is about applying the judgement you have developed with more time to a large extent. Note that when you are a very strong player, blitz is effectively a lot slower and might be more productive, but when your games are being decided by who makes the biggest blunder, you can't be learning much more than to avoid the worst blunders (and experience shows this is hard to do).
"For many people with little time for chess the default option is internet blitz, in which the players have five minutes or less for the entire game. I cannot warn too strongly against taking this route if you want to improve, the problem being that playing too many games at a fast time limit will corrupt the decision making process. Instead of playing good moves, a player honed on blitz will look for moves he can make quickly and perhaps bring himself closer to a win on time. Needless to say, this is not a good way to play 'real' chess, and the habits acquired at faster time limits do spill over." - GM Nigel Davies (2010)