Hello dxe, and welcome to AnandTech Forums.
No gaming, so any basic graphics solution would do
You said it.
For non-gaming (and I guess non-HTPC) you won't notice a difference.
For gaming, well, the G840 HD graphics (it isn't called HD 2000 because it is missing Quick Sync, but otherwise should be the same in games) is about 2/3 the performance of the HD 3000. The HD 3000 is mostly as good (even a hair better) than the Radeon 5450.
The Radeon 5450 is a hair faster (maybe 5-10%?) than the Radeon 4350. They are near identical, but the 5450 has faster DDR3 memory versus DDR2 (800MHz versus 500MHz data rate) and a bit higher clock speed.
Thus, I would say that your Radeon 4350 will be faster than the 6EU HD graphics of the Pentium G840 in gaming, by maybe anywhere from 10-30% depending on the game. This is purely my guess, so take it with a proverbial grain of salt.
In non-gaming use, you will not notice a difference.
Using a Radeon 4350 will add up to 20W to your power draw.