Character Creation
I think I will try for a Mountain Dwarf Barbarian, Path of the Totem Warrior (Bear).
STR 14+2
DEX 13
CON 13 +2
INT 9
WIS 13
CHA 10
Rolls
Attributes - (4d6, 4d6, 4d6, 4d6, 4d6, 4d6)
4d6 : (6153) = 15
4d6 : (1355) = 14
4d6 : (3133) = 10
4d6 : (3454) = 16
4d6 : (2351) = 11
4d6 : (5262) = 15

Also, can we use UA (Unearthed Arcana) material? I'm looking at the UA Revised Ranger with the UA Primeval Guardian Conclave, so that's a bit of an important question... xD
Without further ado...
Rolls
Stats - (4d6, 4d6, 4d6, 4d6, 4d6, 4d6)
4d6 : (3553) = 16
4d6 : (3311) = 8
4d6 : (6126) = 15
4d6 : (2425) = 13
4d6 : (6464) = 20
4d6 : (5513) = 14
Edit: Hopefully I read the reroll 1's correctly. I only rolled for 2/3 because I got max for one of the 1 roll.
Final Stats:
13
11
18
12
17
17
Rolls
Stats - (4d6, 4d6, 4d6, 4d6, 4d6, 4d6)
4d6 : (4454) = 17
4d6 : (2236) = 13
4d6 : (1666) = 19
4d6 : (2341) = 10
4d6 : (6316) = 16
4d6 : (6365) = 20
Reroll 1's - (2d6)
(55) = 10
EDIT: after 1s rerolls...
STR 16
DEX 13
CON 14+2
INT 11
WIS 15+1
CHA 13
Rolls
Stat Re-Rerolls - (4d6)
(5514) = 15
Stat Reroll - (1d6)
(3) = 3
EDIT: won't be much, apparently.
EDIT: I've decided to go Hill Dwarf, and my CON is a bit higher so should be +3 to each of those.
Rolls
HP Increase - (1d10+2, 1d10+2)
1d10+2 : (1) + 2 = 3
1d10+2 : (5) + 2 = 7
4d6 - ( 6, 1 2, 5, 3 ) = 14 (no change)
4d6 - ( 1 3, 3, 5, 5 ) = 13 (no change)
4d6 - ( 3, 1 3, 3, 3 ) = 9 (no change)
4d6 - ( 3, 4, 5, 4 ) = 13 (no change)
4d6 - ( 2, 3, 5, 1 6 ) = 10 changes to 14
4d6 - ( 5, 2, 6, 2 ) = 13 (no change)
New stats after racial modifiers:
STR 16
DEX 13
CON 16
INT 9
WIS 13
CHA 13
Rolls
Reroll 1s - (4d6)
(2316) = 12
Reroll 1 - (1d6)
(3) = 3
18, 10, 11, 17, 16, 12 ... NOT BAD!
Rolls
Stats - (4d6, 4d6, 4d6, 4d6, 4d6, 4d6)
4d6 : (6266) = 20
4d6 : (5223) = 12
4d6 : (1423) = 10
4d6 : (6563) = 20
4d6 : (4662) = 18
4d6 : (3236) = 14
reroll the 1 - (1d6)
(4) = 4