What IP addresses to use for monitor the availability of Internet connection

Sounds like you're talking about Windows, eh?

PING sends ICMP echo request datagrams to the destination host specified. The destination host will send back ICMP echo reply datagrams, if it is so configured. People typically think of using PING to judge the "reachability" of a host. You can vary the size of PING packets and watch the round-trip time to learn a little about the network bandwidth conditions (as well as, obviously, measuring latency) between the source and destination hosts.

A rookie mistake, BTW, is thinking that because you never receive a reply your echo request datagram isn't getting to the remote host. The absense of replies tells you that your echo request didn't reach the destination host OR the reply from the destination host didn't make it back to you. The absense of PING replies doesn't tell you anything conclusive.

The Microsoft TRACERT utility seeks to provide similiar functionality to the Unix "traceroute" utility. Microsoft's TRACERT sends out ICMP echo request datagrams with increasing "time to live" (TTL) values. The TTL determines how many hosts an IP datagram can be forwarded through. Each host that forwards the datagram decrements the TTL until it reaches zero, at which point the host that decremended the count to zero sends an ICMP time to live exceeded datagram to the host that sourced the datagram that has ceased to "live". By sending out datagrams with increasing TTL values and watching where the time to live exceeded datagrams come from one can produce a "map" of the "hops" that the outbound datagram moved through, along information about how long it took for the datagram to round-trip.

Incidently, the Unix "traceroute" uses UDP datagrams rather than ICMP to perform a similar function.

Packet loss tells me that something is malfunctioning somewhere, likely a switch or the modem itself. Depending on what you're doing, a DSL connection should be adequate for 50 users just surfing the Web: I have several clients on standard business class DSL connections (5Mbps down, ~800Kbps up) with ~100 users using the Internet for standard Web surfing and email and performance is fine.

I do find that I regularly swap out DSL modems, regardless of manufacturer: they just seem to be cheaply made, get pretty hot, and die eventually. Might be worthwhile as a quick test to swap in another DSL modem.

If you're a heavy Internet user (lots of downloading/uploading of large files, etc.) and with two DSL connections, I'd recommend getting an edge router that can do load balancing/failover and possibly Quality of Service (QoS): Netgate sells ALIX kits with pfSense (Open Source) firewall, which has "enterprise" features for ~$200 USD. Best bang for the buck for a firewall I've seen. With that configuration, you can even setup policy-based routing to route certain traffic out one connection primarily (say, core server services like email, DNS, etc. get routed out through DSL #1, web surfing out #2), while failing over when it's down.