Breast Milk on the go 🍼

I'm due in less than 4 weeks & plan on exclusively breastfeeding for at least 4-6 weeks before I introduce a bottle. I'm not going to be comfortable breastfeeding my baby in front of others, other than my husband & sister inlaw. I plan on pumping so when we go out visiting our little one will be feed without everyone staring while she eats, even with a cover. Yes I fully understand breastfeeding is 100% natural, but I'm not comfortable doing that with a bunch of people around & staring! My main question is for those of you that are like me or ones that just pump, how did you take your milk when you went out? & how did you take the milk? was it frozen or freshly pumped & kept cold? Did you use a cooler bag, something else or did you get special diaper bag that has a special cooler section in it? I'm sorry if this sounds confusing, I'm a first time mom & this is all new to me and I've never been around someone that breastfed so I have no one else to ask. Thank in advance!!☺