EDITED: As per Nails post below
I think we can all agree that the whole point of the expertise and magic item progression is so that we have an even growth in power as possible. The goal then is to try to manipulate the system in such a way as to get that even progression. Assuming my math is correct, I think the process below is the most effective way of getting an even power progression. Therefor, any deviation from this will result in a relatively over powered or under powered character. Use it as you will, but in the end I think one thing is clear, assuming no other reliable outside bonus to hit, expertise is definitely needed,
Heroic
Average Monster AC = 14+Level
Average PC Attack Bonus = Mod+Proficiency+1/2 level+Magic+Expertise
Code:
Assumed PC attack vs average monster AC at level 1:
4+2+0+0+0=6 vs. 15=14+1
Chance to hit = 60%
Assumed PC attack vs average monster AC at level 2:
4+2+1+0+0=7 vs. 16=14+2
Chance to hit = 60%
Assumed PC attack vs average monster AC at level 3:
4+2+1+[B]1[/B]+0=8 vs. 17=14+3
Chance to hit = 60%
Assumed PC attack vs average monster AC at level 4:
4+2+2+1+0=9 vs. 18=14+4
Chance to hit = 60%
Assumed PC attack vs average monster AC at level 5:
4+2+2+1+[B]1[/B]=10 vs. 19=14+5
Chance to hit = 60%
Assumed PC attack vs average monster AC at level 6:
4+2+3+1+1=11 vs. 20=14+6
Chance to hit = 60%
Assumed PC attack vs average monster AC at level 7:
4+2+3+[B]2[/B]+1=12 vs. 21=14+7
Chance to hit = 60%
Assumed PC attack vs average monster AC at level 8:
[B]5[/B]+2+4+2+1=14 vs. 22=14+8
Chance to hit = 65%
Assumed PC attack vs average monster AC at level 9:
5+2+4+2+1=14 vs. 23=14+9
Chance to hit = 60%
Assumed PC attack vs average monster AC at level 10:
5+2+5+2+1=15 vs. 24=14+10
Chance to hit = 60%
So it seems like there is a lot less swing if you give the players a better magic item at levels 3 and 7, but in order to maintain a 60% chance to hit it is still best to give the players expertise at level 5. Alternatively you could give the players a better magic item at level 5 instead of 7 and take expertise by level 7, but I think its clear that expertise is needed.
Paragon
Average Monster AC = 14+Level
Average PC Attack Bonus = Mod+Proficiency+1/2 level+Magic+Expertice
Code:
Assumed PC attack vs average monster AC at level 11:
5+2+5+[B]3[/B]+1=16 vs. 25=14+11
Chance to hit = 60%
Assumed PC attack vs average monster AC at level 12:
5+2+6+3+1=17 vs. 26=14+12
Chance to hit = 60%
Assumed PC attack vs average monster AC at level 13:
5+2+6+3+1=17 vs. 27=14+13
Chance to hit = 55%
Assumed PC attack vs average monster AC at level 14:
[B]6[/B]+2+7+3+1=19 vs. 28=14+14
Chance to hit = 60%
Assumed PC attack vs average monster AC at level 15:
6+2+7+3+[B]2[/B]=20 vs. 29=14+15
Chance to hit = 60%
Assumed PC attack vs average monster AC at level 16:
6+2+8+3+2=21 vs. 30=14+16
Chance to hit = 60%
Assumed PC attack vs average monster AC at level 17:
6+2+8+[B]4[/B]+2=22 vs. 31=14+17
Chance to hit = 60%
Assumed PC attack vs average monster AC at level 18:
6+2+9+4+2=23 vs. 32=14+18
Chance to hit = 60%
Assumed PC attack vs average monster AC at level 19:
6+2+9+[B]5[/B]+2=24 vs. 33=14+19
Chance to hit = 60%
Assumed PC attack vs average monster AC at level 20:
6+2+10+5+2=25 vs. 34=14+20
Chance to hit = 60%
So this time a new magic item at level 11, 17, and 19 along with the bonus from expertise help balance every thing out most of the way.
Epic
Average Monster AC = 14+Level
Average PC Attack Bonus = Mod+Proficiency+1/2 level+Magic+Expertice
Code:
Assumed PC attack vs average monster AC at level 21:
[B]7[/B]+2+10+5+2=26 vs. 35=14+21
Chance to hit = 60%
Assumed PC attack vs average monster AC at level 22:
7+2+11+5+2=27 vs. 36=14+22
Chance to hit = 60%
Assumed PC attack vs average monster AC at level 23:
7+2+11+[B]6[/B]+2=28 vs. 37=14+23
Chance to hit = 60%
Assumed PC attack vs average monster AC at level 24:
7+2+12+6+2=29 vs. 38=14+24
Chance to hit = 60%
Assumed PC attack vs average monster AC at level 25:
7+2+12+6+[B]3[/B]=30 vs. 39=14+25
Chance to hit = 60%
Assumed PC attack vs average monster AC at level 26:
7+2+13+6+3=31 vs. 40=14+26
Chance to hit = 60%
Assumed PC attack vs average monster AC at level 27:
7+2+13+6+3=31 vs. 41=14+27
Chance to hit = 55%
Assumed PC attack vs average monster AC at level 28:
[B]8[/B]+2+14+6+3=33 vs. 42=14+28
Chance to hit = 60%
Assumed PC attack vs average monster AC at level 29:
8+2+14+6+3=33 vs. 43=14+29
Chance to hit = 55%
Assumed PC attack vs average monster AC at level 30:
8+2+15+6+3=34 vs. 44=14+30
Chance to hit = 55%
Since we gave out the +5 magic weapon in paragon we only have the +6 weapon at 23, plus the boost from expertise at 25, but as you can see the progression is pretty even.