Have a read
EOS 400d/ D40 or a prosumer model
The advantage of the Bridge would be the range and not nessesarily quality of its built in lens (others would be cost as you've noted , and size)...
Oh.....with a DSLR .it is unlikely you'd stop at the camera too... eventually
Although my situation was different from yours ( having been into Photography for years prior),
I had a comparable scenario a few years ago
Back then I had a (now unused) Fuji 602Z and was at a send off party where a colleagues husband came with his Canon 300D .
A few days later we got to compare identical Pictures ( I had taken shots with his camera as well as mine)
The sheer detail and noise free quality of images (no PP) from his camera compared to mine (enhanced in Software) was to ensure that the 602 would be my last non-DSLR.
Saying that, I have used a friends
Canon Pro one ( high end Bridge) which comes with a 28- 200mm L lens, which is far better in quality and range than the Kit lens from the 350/400/30D .
I was a bit less impressed by its slightly greater shutter lag and somewhat greater noise at higher ISO (max 400

) , but in modest light conditions it is a compact unit which proved very capable. (It had a "noisier" Sony sourced 8Mp CCD as opposed to the 8Mp CMOS used in the 350D)
It was more than £250 in its heyday though
HTH