Step 1: List the fixed anchors first.
G must be in Travel (e). C must be in Travel or Beauty, not Tech (b). A cannot be in Beauty (j). F is not in Travel and must join exactly one of A or B (d).
Step 2: Keep C and B together.
Condition (i) forces C and B onto the same team. Since C cannot be in Tech, the C-B pair sits in either Travel or Beauty.
Step 3: Decide where F goes.
F is barred from Travel and must accompany A or B. If F follows B, then F joins the C-B pair, giving a natural Beauty trio B, C, F.
Step 4: Check A and B are apart.
Condition (a) says A and B are on different teams, and (j) keeps A out of Beauty anyway. So placing B, C, F in Beauty keeps A elsewhere, satisfying both.
Step 5: Verify F's single partner rule.
F is with B but not with A (since A is not in Beauty), so F is with exactly one of A or B, satisfying (d). F is also not in Travel, which is fine.
Step 6: Match against the options.
The Beauty team that satisfies every relevant clue is B, F, C, which is exactly option 1.
\[ \boxed{\text{B, F, C}} \]