Yes, going for the Sigma 18-250 "Macro" or the Tamron 18-270 PZD. Both have stabilization. Both are within range, economically. About $350 used. Twice that new. If the one I get with the 5100 is on the same receipt, I can get damage insurance on it.
A second lens will be a 50mm f/1.8. Nikon, Sigma, and Tamron all offer these. Can't afford "L". Regular should be ok.