Jazz music question - (Grand Theft Auto 3)

I’m going to start by admitting I know absolutely nothing about jazz, so I may be barking up completely the wrong tree here. Anyway, on to the question.

I have always loved the music that plays over the introduction credits of PS2 game Grand Theft Auto 3. I’m at work, so I’m not sure I can link to anywhere it may exist on the net, but for those that don’t know it, it (to me at least) has a bluesy, jazz feel to it, with a rhythm based around a simple piano riff, complemented by, to my ears, a muted trumpet.

I’d love to find more music in this style but have absolutely no idea where to start. Do any of you have any suggestions for artists or songs to try?