I've bought the ut61e mainly because of its serial interface. It has better resolution as well (22000 counts vs 6000 counts of the ut139c) but as a first meter I would recommend the UT139C over the UT61E as it has back-light and temperature probe, features that you may find more useful. Both meters offers mV and uA ranges, useful if you want to work with battery powered circuits, but the UT139C has a slightly better input protections (more relevant if you intend to probe mains power, what I do not recommend) and, more important, it is cheaper.
Regarding the built quality, both are equivalent and fairly well made.
Inevitably, you will find very soon that one multimeter is not enough and you will need a second one (then third...
), then you can start looking for more advanced meters with features tailored for your needs.