I just bought a Lenovo Thinkpad E430 and want to install Ubuntu in it. But I don't know whether I should install 32 bit or 64 bit.
Its core i5 3rd generation and 6gb ram (2 + 4)
I would install the 64-bit version. Looking at the spec sheet it's using the Intel i5 & i7 CPUs (depends on which Type-Model you have).
All the Intel i CPUs are now 64-bit so it really doesn't make sense to use anything except 64-bit on this hardware.
Looking at the PDF Spec, and given you have one of the 4GB+2GB models you can only have the i5-2450M processor.
This particular processor is only 64-bit, as stated on the Intel Specs.
Performance improvements of 32-bit vs. 64-bit in the early days were sometimes the case, but this has largely been relegated to only very specific applications and cases. In general it's not the case.
If you're interested, I typically look up a CPU on cpubenchmark.net to get a sense of where a processor stacks up. Especially if I'm contemplating putting a 32-bit OS on 64-bit hardware. Also because it's fun just to look at this kind of stuff if you're into computers & technology 8-).
Given the following:
I would definitely install the 64-bit variant of whichever OS you decide to go with.
There used to be a time that running 32 bit made more sense as some of the applications would not work (well) under 64 bit. Special drivers for hardware, video- and audio-decoding, and applications like skype might not run properly.
From my experience the video and audio related issues are a thing from the past, drivers might be a problem though for new hardware if the drivers have to come from the hardware manufacturer.
I would install the 64 bit version, as this allows you e.g. to run 64-bit guests in VirtualBox.