Well I went true some lenses over time.
I started with K20D + DA*16-50 and DA*50-135
My first prime was the DA40 and that killed the use off the 16-50, plain because off IQ and ease off use for the smaller lens.
I bought the DA*60-250 because I neede some longer lens and had an opertunity for second hand. The 50-135mm never left my house again. The 60-250mm is better in all regards except for the f2.8-f3.5 part where the 60-250mm can't come. I also bought the FA*85mm in this range.
Made a thread about it:
DA*60-250mm/f4 test
Then I bought the DA*300mm and this makes toast off the 60-250 at the long end at f4. You gain more in length, since the DA*60-250 is only 250mm when focussing toward infinity.
Then I bought the Sigma 70-200mm/f2.8 EX DG OS HSM because off the f2.8-f3.5 range, wich for me mainly is only using it on f3.2 for indoor sports. At that time while the DA*60-250mm is the better lens it didn't gave any use and I sold it.
I guess that I would have use for a DA*135mm/f2.0 and sell the Sigma at that time again.
So looking at your request I would say to buy the DA*60-250.