I acquired an old laptop with an AMD-K6-something @ 366 with 160 MB of RAM. It is dual-booting fresh installs of Windows 98 SE and Windows XP SP3.
160 MB of RAM is very little amount for WinXP. All browsers that uses XP benefits will eat all your RAM in few seconds. Only IE6 or older Mozillas (such as Firefox 2, SeaMonkey 1.1 or Mozilla 1.7) might be usable and not too slow. But they are not well compatible with modern sites. Because almost all modern websites are using forced strong encryption (TLS 1.2 256-bit), they are require a browser that supports the strong encryption.
All Gecko-based browsers from 2006 and later are compatible with modern websites out of box. They cannot run most scripts and other active content, as they are based on latest versions of jQuery, but the text and pictures should be visible. And they are working really fast.
To use IE6/7 or Opera on WinXP SP2 or SP3 with the modern web there are two important updates: KB968730 and KB3055973. Some people say that only KB4019276 may be useful, but I'm successfully added the support of TLS 1.2 256-bit to XP SP2 with the two previous updates. IE6 SP2/3 is the most fastest browser for XP, but it is from 2004 and it has very bad renderer that is working very bad. IE7 is a something better, but it likes to freeze the system. IE8 does not require TLS updates and is compatible with almost all modern sites, but it consumes big amount of RAM. Operas 8...10 are working like Firefox 2, but some sites are displaying as a blank white page due to bug in the renderer of Opera.
Only Opera 12 (even on Windows 2000) does not requiring the TLS updates and is working with the modern web almost perfectly. But it is very slow on old hardware. Even on P3-933 with 1024MB of RAM it works very sloooow.
2×Soviet ZX-Speccy, 1×MacIIsi, 1×086, 1×286, 2×386DX, 1×386SX, 2×486, 1×P54C, 7×P55C, 6×Slot1, 4×S370, 1×SlotA, 2×S462, ∞×Modern.