We use laminated bars because they are a lot lighter than a solid one. But the Solid Steel bars are a lot more durable and less prone to bending and quite heavy. When you are milling the weight of the piece of wood you are cutting can sometimes pinch the bar and make the clutch slip but I just put a wooden wedge or felling wedge in between Solid Steel bars will probably hold up to the pressure better but you should wedge it anyways. You will probably be fine with a laminated bar especially if you are just getting into milling, just use wedges. If you are set on a Solid Steel bar then Granberg (GB) And Tsumura make them, even some Husqvarna bars are made by GB.
Another reason for the Solid steel bars could be because the mill clamps to the bar and that could possibly pinch your bar but if you put it on correctly it shouldn't do that.
I'm Assuming you meant 029 but an 019 would mill so slowly and put so much wear on it and its a top handle so use a different saw if you just have a 019. An 029 wouldn't be that bad. I used a 50cc saw for milling a while ago and it did quite well although it was all pine slabs. Just to try it out to see if you like it than I wouldn't worry to much, just don't push the saw really hard let it work for itself. You could also always get a bigger saw too even some used 70cc would be decent. Make sure to let the saw idle (not shut off) to circulate air around the saw for a minute after each slab and always make sure you have bar oil in your saw. And if your saw is running lean you will blow your saw so quick so make sure your saw is running rich. Also If you are using a small saw or really any say for milling pick it up with one hand on the mill and one on your saw because you don't wanna break your bar studs or any mounts.