There's little usefulness to arbitrarily moving your legacy addressed funds. You might as well let them sit until you need to spend them. You'll have to pay a miner's fee either way. If you don't move them, it'll be one legacy level fee (per UTXO). If you do move them, it'll be one legacy fee and one SegWit fee.
About the only reason to move them is to arbitrage transaction fees. You might consolidate several legacy UTXO's into one SeqWit address when fees are low so that you can save money in the future when fees might be high. Or you might convert using a very low fee that takes days to confirm so that you can promptly pay an invoice at a high satoshi/byte rate, but at a lower total cost.