My kids have always liked the Applegate Farms but that's all they've ever had. I bought some ordinary brand once because it was cheaper and they wouldn't touch it. The "slime" on the Applegate is just gelatin. It is present on many deli meats before slicing. I was grossed out by this when I worked at a deli in college but then a depression-era older lady I worked with explained that the gelatin helped keep things fresh and moist.
I don't buy lunch meat very much because it is a costly form of meat, and even the uncured ones have compounds that are not known to be safe in large quantities. Several years into packing lunches, we've done fine without it and my kids never ask for it. Sometimes I'll slice some roast chicken or leftover cold steak thinly and sprinkle salt over it, and they love that. I think if they'd been allowed much processed meat while they were little, they would be less willing to eat regular meat.my sister only and often ate processed meats when she was little, and this was before the days of uncured/organic. I know, bad parents

Anyway my sister never did become accustomed to eating natural meat. She's now a vegan - go figure.
That said, many toddlers do not seem to like the texture of ordinary meats. That's ok. But I think it would be better to introduce meats that are soft but do not contain too many additives and sodium. Fine textured meatloaf with moderate fat content, fine bolognese, turkey patties, homemade gyro meat, and homemade sausage are a few ways my kids enjoyed meat while in the toddler stage.