Your Thomann kit turned out pretty good so I doubt you will have any trouble with the new one.
Assuming that your new kit is a bolt/screw on neck it probably came with a neck plate. Just position the plate, clamp the neck and the body together and use the neck plate as a guide to drill your holes, making sure that you don't drill too deep into the neck.
Don't worry too much about no drill press, there are plenty of us here (me included) that don't have one. Just try and hold the drill as vertical as you can. Wood is fairly forgiving.
IMPORTANT: Make sure you lubricate the screws before you tighten them up, especially for the first time. I just use candle wax, but there are probably better solutions out there.
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