The clunkiness is probably due to the low hardware specs of your machine (and the inefficiency of the engine, but that can't be helped). This also limits the amount of mods that I could recommend since many mods would require a beefier machine.
There was a mod called
Streamline which I used on my old PC, it made gameplay smoother. However, it's very old now, it never went out of beta, it may cause occasional crashes, and it needs OBSE (Oblivion Script Extender) to work at all. There may be better alternatives by now, my info about Oblivion is several years old.
With regard to other mods: I suggest to play the game a bit without mods, but don't invest too much in the character you do that with. The unmodded game becomes rather silly once you realize how broken some of the mechanics are, but it's fun until you reach that stage, and playing unmodded for a while will allow you to make better decisions about the mods you want.
Personally, I was using FCOM, which in itself is an amalgamate of Oscuro's Oblivion Overhaul (fixes a lot of the silliness mentioned above and adds lots of new stuff), Francesco's mod (adds tons of new items), Martigen's Monster Mod (tons of new enemies and smarter / more plausible behavior of them), Warcry (more enemies and items) and an armory mod that adds more weapons and armor. I also used a levelling mod (since I couldn't stand the way the unmodded game handled skills and perks) and an economy mod ("Living Economy", dynamically adapts item prices over time, might be outdated by now). I also remember using COBL (general framework for more items IIRC), and mods that added more hotkeys, bundled the mess of in-game keys in a keyring, or allowed the complete change of one's gear with a single keypress. Then there were some companion mods I quite enjoyed, and of course graphics mods for enhanced view distance, but the latter won't do any good with the graphics chip you're using. But as I said, there are tens of thousands of mods, so perhaps play the game first, and then decide in which direction you want to mod it.