You should focus on your basics movements, lines of balance, and how to generate power.
First, your basic movements (the ones you do at the start of the class) are there because they are used everywhere. Any technique will use a basic move, or a slight variation of a basic move. If you cannot see it, ask someone.
Second, the lines of balance are important: where is uke's line of weakness? This is probably where you should be pushing/pulling uke. Most, if not all, techniques follow a line of weakness. Some kata might assume that uke does a certain thing (for example, pulls back on a grab) so uke needs to know what they are going as well. Again, if you are unsure, ask.
Third, sometimes uke is generous and provides you with plenty of momentum to throw them. At other times, not so much -- for example when you miss your timing point. In that case, you need to provide most (if not all) of the momentum to throw uke. In most cases, power comes from your core muscles which generally is what tanden/hara refers to. If you have a strong core, then throw will be easier. As Philip Klöcking kindly pointed out in the comments, not only is the core the biggest muscle group but the centre of mass of the body is generally close to it. As in Judo, keeping your core low makes it harder to destabilise. This works for both uke and tori.
However, I suspect you are overthinking it. Learn techniques slowly at first, then speed them up, and finally add resistance to make sure that they work.