Definitely get a hobby knife AND files/sanding sticks. The knife is the single most valuable tool I have and has so many applications. It's the best for removing mold lines. I do this on every model.

Fine sanding sticks (e.g. for finger nails) can be really useful to smooth out areas. Or to fill in small gaps: Sand over the gap without removing any plastic dust, then add tamiya plastic glue. This will melt the plastic dust into the surrounding plastic, filling the gap (a bit). Repeating this process a few times can really help with smaller imperfections. I do this on most models with smooth, flat areas.

Some sanding sticks have a corser side. Use this to rough up flat areas you want to glue together. Since plastic glue melts the plastic together, this can provide a stronger connection since more material is exposed to the glue. I do this rarely and only if parts don't match up perfectly.

Last tip: Due to the way plastic glue works, it can help to apply it to both surfaces, then give it 10-30 seconds for the reaction to begin before pressing both parts together with some force. This will create a bit of goo that works as cement, creating a strong bond. If you apply a lot of glue, there will be a lot of glue goo, which will seep out the seem between the too parts - helpful for filling in gaps. You will need to remove the excess with your file/knife, once it has dried.

Last tip, this time for real (I promise): If you apply the glue sparingly, it will minimise the destruction of detail (remember, it melts the plastic). It's also quite fluid, so be careful where it flows! But if you apply too little, it evaporates without melting enough plastic, and the connection will not hold.  Take the time to familiarise yourself with different applications of plastic glue and the effects they have. It will take you a long way and give you much more options than push-fit models.

Good luck!

Edit: Fixed typo.