I would pick an i5 instead of an i3. I5 is the better future proof by far and also has the better price/performance value by far. (i5 4460, i5 4590 or i5 4690, get the cheapest) Unless you have a big budget issue, go with the i5.
Lag? This is difficult, it depends on the game you play, game settings and many other factors but the PC based on i5 will obviously have the less probability of lags. Your GPU also play a role in lagging.
Overheating? It depends on the cooling system you have (case, air flow, dirt, cooler fan, etc.). Usually even with the stock cooler, if you build your PC correctly, meaning, everything is mounted correctly. You should not have this problem with the PC in your link.
Noise is something else, you need to invest on the correct case, fans, etc. in order to build a silent system.
Loudness is also relative. Take a look at my rig (hover your mouse cursor above my avatar), my rig is really silent.