As in every case, if you purchase separate tickets for your itinerary, make sure you have travel insurance that covers you in case of delays. Other than that, there is the inconvenience of probably having to recheck your bags in HEL if you travel with checked luggage.
If you can catch a direct flight from wherever you are going to Tampere and drive from there, that is a good option. If you are arriving to HEL and then connecting to Tampere, to then get a rental car from there, you might as well get the rental car directly from HEL. Driving time to Pori is around 3 hours, compared to about 1:30 from Tampere. This means you won't save a whole lot of time by flying the extra segment, and more segments means more chances of delays and missed connections etc.
As a third option you could check out
VR: Junamatkat verkkokaupasta. Katso aikataulut ja osta lippu. - VR for train tickets. They offer fairly good frequency at moderate speed, but the hassle is that there is no train station at the airport in HEL, so you need to get a bus or a cab to the nearest train station which is Tikkurila.
Good luck and tervetuloa Suomeen!