Is that "spare" modem intended for a laptop or is it simply an external modem that can be used with any computer?
To use a 28.8kbps modem, you'll need to setup a dialup Internet connection for your ISP in Windows 95. Does your ISP provide dialup numbers?
Even though using that modem would yield a very slow Internet connection, that laptop would have difficulty handling a DSL line at full DSL speeds. Web browsing would be choppy/jerky. Still, an actual DSL connection might provide a much faster web browsing experience than the 28.8 modem.
However, if you were able to actually use the DSL connection on that laptop, you need to consider other things. Can you find firewall software that will run on it? I rather doubt it. And, what about spyware removal software and anti-virus software that will run on it? I suggest forgetting the idea of using that laptop on the Internet except perhaps as a backup computer for Internet access via the 28.8K modem in case you can not get online with your main computer.