I love lululemon's The Towel. I think it's $28. Not cheap, but it works for me. I have also found inexpensive towels at Marshalls. I think I prefer the lulu one, but my Marshalls one was half the price and it's decent. For hot yoga, I don't use a bag because I want my mat to breathe a little before I get home. I like the lululemon mat straps.
I have a Manduka towel that I love. I have a Manduka Prolite mat - which is still crazy slippery (but getting less so) even after a few months of use. I probably would try the Mat from LuLu next time I got a mat.
When I did hot yoga, I loved my Mysore rug to deal with slippage and sweat. Now I just use it for savasana, but it's 12 yrs old and you'd barely know it, just a little fading (I have Jaipur).
I recommend lululemon's The Mat for hot yoga. It's heavier and thicker than a typical yoga mat, but I don't slip at all. It's great. I also have the mat straps to cart it around, as it doesn't stay rolled up on its own. It is more expensive at around $70, but I justify the cost on the fact that I'd probably spend that much or more on a pair of shoes if I were doing any other activity.