I've done one for my bed in Sirdar Calico which is a cotton acrylic mix, very soft and can be tumble dried. I have no idea what it cost as I bought the yarn as I went, but I think it would fit your budget.
Wool blend? Does it need to be machine washable? DK or aran weight?
For a washable soft yarn, the stylecraft is great TBH. Wendy Merino DK is washable and very very soft but I suspect it will pill a lot and the mitts I made have stretched quite a lot. The Aran yarns that come in a massive 400g ball are nice, 20% wool and washable.
For baby yarns, I like the King Cole Comfort which is very soft and cuddly and cheap, around £3/100g and nice to knit up, has washed well for me.
I would love to crochet an afghan in lovely soft wool, but I've got to stick to a budget. I want something nicer and softer than Stylecraft Special, which is my normal yarn, but can't afford cashmerino etc. What yarns would work? I'm willing to pay maybe £3.50/50g (but cheaper would be better.) Would a baby yarn work for an afghan? Help, please.