Fortunately, though both groups twist and misunderstand Scripture, they both accept it as authoritative. For this reason, you have a middle ground which you can use to create productive dialogue. This means good exegesis and hermeneutics on your part.You are also going to want to know your early church history, particularly with LDS.
JW are clever evangelists. The beautiful thing with them is that you dont have to approach them in order to spread your faith–they’ll approach you. When they bring up their faith make sure you bring up yours. As you dialogue, agree on issues that are common, but press them on issues that differ. The Gospel of John is especially helpful as well as the epistle to the Hebrews, and much of the Pauline Epsitles
LDS, the same is true for them. They’ll want to approach you, and if you approach them they’ll be flattered and welcoming I’m sure. LDS can be harder to deal with. They actually have scholarship at Universities backing their version of apologetics. If you come across a knowledgeable Mormon, it could be interesting. I had a professor, Carl Mosser, who is a Theologian, Apologist, and NT scholar whose greatest works were Mormon apologetics books. You might think about looking into his work.
Don’t think because these groups are erroneous that they won’t make good points. If you come across the right one you may very well have a rigorous argument on your hands. Just know that both groups have their own version of apologetics and anti-apologetics in which they are generally well trained in order to aid them in their evangelism which is heavily emphasized by both. Every week they go to “church” they are trained to be able to engage and refute people like you. Thinking about your post thought, you said you were familiar so you probably already know of this. If you don’t want to approach them they’ll approach you, just be welcoming and make yourself available.