I buy and sell children's clothes on eBay all the time. I post them in plastic mailing bags and send them by second class post ( or Airmail obviously). Up to 750g costs £2.20 and I charge another 10p to cover the cost of the mailing bags. 750g is a lot of baby clothes, so I tend to sell things in small bundles (3 long sleeved tops, 2 pairs of shorts, 4 sleepsuits) or outfits (dress, cardy and tights). Apart from outfits, I tend to find that bundles of mixed tops and bottoms don't sell well ( I think because sometimes babies are a different size on top to bottom).
I get the mailing bags from eBay, and usually buy a pack of about 30 in assorted sizes. It is much easier and quicker to use these than it is to wrap lots of parcels.
If you are careful, small items like T shirts, swimming trunks etc can be folded flat into an A4 or A5 envelope and go for £1 (A4 a bit cheaper), but there are thickness limits and you need to make sure the item doesn't slump in the envelope and make it too thick anywhere, even if it is thin enough when laid flat.
I find that if you are selling small, relatively low value items then people don't really want to pay another £1 for recorded delivery. Large, high value items (coats, well known sought after brands) it is worth getting recorded delivery, but remember ordinary post is insured up to £50.
I have found a lot of success just listing everything for 99p (free) and seeing what happens. Best thing is to have it finishing at 8-10pm on a Sunday night. And make sure you put the make in the listing title - I search particular brands because I know what fits my lanky son and roundier DD eg: " 12-18 months, Next boy's red winter coat" gives a lot more information quickly rather than "Winter Coat", even if you put the other info in the item specifics. Just gives another way of searching foe people with a smart phone in one hand and baby in the other (your main audience!).