I also recommend starting with Symphony. That's where I started reading UF to Peggy some 15 years ago, and she had no problems (other than the occasional "oh, geeze" at first when she saw a source she knew ) getting into the setting.
Rajvik, I also recommend staying away from the Core stories at first. They're a different beast entirely from the later material, and not just for stylistic or skill-level reasons -- late in the Core there is what amounts to a rewrite of the entire cosmos which produces the universe in which the later stories are set. Much of the Core is quite literally in a completely different fictional setting from the rest of the material in UF. This can be confusing unless you're ready for it.
-- Bob
---------
Then the horns kicked in...
...and my shoes began to squeak.
Rajvik, I also recommend staying away from the Core stories at first. They're a different beast entirely from the later material, and not just for stylistic or skill-level reasons -- late in the Core there is what amounts to a rewrite of the entire cosmos which produces the universe in which the later stories are set. Much of the Core is quite literally in a completely different fictional setting from the rest of the material in UF. This can be confusing unless you're ready for it.
-- Bob
---------
Then the horns kicked in...
...and my shoes began to squeak.