I am going throught the same issue as you. I started by adding Boston (ISTS) tweeters running off the stock amp and caps(crossover.) The stock tweeters just didn't sound right. My Sony drives them fine. I added a dash mat to soften the center speaker (seemed too much out of level with the others) and poly filled the sub to get rid of that hollow bass sound. I can live with this for a while, and it was cheap to do. Still will upgrade speakers next (maybe with an amp.)
Speakers make the biggest difference in your sound. Don't cheap out on them, but know that some of the better ones really need more power than what the Sony will push out, and an amp will really make them sing. That said, the Sony head unit is decent. Yes aftermarket makes way better, but the $$$ you need to spend to get there is rather high. Stick with Alpine head units if you go that route.
An amp will help the speaker sound even better (much more so when combined with an aftermarket head unit.) I will add more speakers and amp when I get the chance and $$. The head unit will be the last thing I replace. Just my plan, but has worked in past vehicles I have had.
If you don't plan on upgrades after the speakers, you can get by will less expensive ones that should sound better than the Sony's. I was never a fan of Sony speakers. They are o.k., but not great.