I'll answer the question generally, since individual products may, as you suggest do a little looking around without telling you. You might want to watch the activity lights when you connect, and try to correlate them with the connection sequence.
I'm assuming here that you have the commonest sort of arrangement, a router (connected to DSL, cable ? etc) and a laptop with a wireless client radio inside.
Every 'access point' (one type of radio operating mode) must broadcast a beacon signal to tell possible client radios in range something about itself. For 802.11 b/g (and probably n, but I haven't checked) the beacon is broadcast on the only channel that is legal everywhere, channel 10. It's also broadcast with the lowest possible legal speed. This means that any client 802.11 b/g radio in range will be able to hear and understand the beacon.
Once the client radio hears all the local beacons, it chooses one (usually based on signal strength) that it can interact with. So an 802.11b client radio, which knows nothing about 802.11g format signal types (ie, 'modulation schemes') won't be able to work with an 802.11g access point and both had better be willing to find the highest performance connection possible to both, in this case one of the 802.11b schemes, and not any of the 802.11g expanded schemes.
This takes a bit of time. but once both ends have discovered the highest performance configuration they can both support, the radios can actually tell the software (drives, operating system, ...) what's going one. At that point, Ip addresses have to be assigned to allow any traffic to and from the Net. If the Operating system is configured to use DHCP, it must contact the DHCP server it's been told about, and 'lease' an IP address from the block of addresses the ISP has had assigned to it. Next time on the ISP, the IP address assigned might be entirely different. Or the Internet software using the client radio might have been given a permanent IP address (called 'static' address assignment in contrast to the 'dynamic' assignment under DHCP).
All of this takes time. Which further depends on the connection scheme (speed, modulation, etc) the radios have agreed on. So a marginal 802.11b connection (distant location, poor antenna placement, bad polarization match, ...) might only be able to manage the barest minimum, 1Mbps. A really good 802.11g connection, could use the highest speed possible. which will of course never be as fast as the ads claim. there is a good deal of handshaking and timeout settings, and error announcement sent back to the other radio when found.
And there is a backoff_and_try_a_lower_speed_connection negotiation when there are more than x errors (varies by manufacturer default, but is sometimes changeable by the user for a particular installation in the case of some utilities and software drivers). And an occasional try_to_use_a_better_speed_ connection if we haven't had errors in the most recent y seconds. Either requires another negotiation sequence, which again takes time.
And, if the range is marginal (almost too far away) there will not only be automatic up regulation attempts, and perhaps some down regulation attempts, but more a few entire reestablish_the_connection restarts as signal drops below the radio's sensitivity threshold (all real world equipment has them).
And some operating systems take their own sweet time to recognize a new device (in Windows, you may have to run the add_new_hardware wizard in the control panel manually. Sometimes the whole add new hardware routine more than once to succeed.
Finally, on initial start up, most browsers depend not only on hardware initialization, connection negotiation, DHCP negotiation, and so on. But also must do a DNS lookup, and download the current versions of a 'home page' (which may be larded with images from many other sites). It can all take a little while, and much of it is worse under wireless protocols than wired (much more chance of destructive interference (eg, garage door openers or baby monitors for the 802.11 b/g specification radios).
And again, your router, your client radio, or some virus or spyware software you have on your machine, might be connecting with just about anyone and hiding it in the connection negotiation sequence, or elsewhere in the startup sequence. Watching the packets sent out during that sequence is the only way to be sure you can see all the data being exported. Use a good spyware remover (or two because they all seem to miss a different group of the intrusive stuff) and a good antivirals program as well. There are freeware products, shareware implementations, and purchase ware designs. The anti-virus products for Linux concentrate mostly on Windows viruses, so as to avoid sending any such to any of the Windows machines the Linux box is supporting (as a file server, perhaps).