According to Crucial, the Dell Inspiron 1525 laptop can actually be upgraded to 4GB of RAM, and there's even a report that it works with 6GB of RAM. For me, the biggest reasons for upgrading to 64-bit are security related: With a 64-bit version of Windows, you get DEP and PatchGuard, which are two technologies that make it more difficult for an attacker to compromise the integrity of your system.
As far as software goes, pretty much all programs written since the Microsoft Windows Vista timeframe (2007) have 64-bit support, and most Win32 (32-bit Windows) programs work fine as well. If you needed to run something older (16-bit Windows 3.1 or DOS apps) there would be problems, though, as they are not supported by the OS anymore.
64-bit versions of Windows tend to use a little more RAM than their 32-bit counterparts; I recall that 32-bit Windows 7 used something like 700-900MB of RAM while at rest, while 64-bit used 1.2-1.3GB of RAM. This means that you would probably have a few hundred MB less RAM to run software if you went with a 64-bit version on a 3GB RAM. As a result, I'd suggest looking into increasing the laptop's RAM eventually if you planned on going the 64-bit route.