A P4 3.0GHz is not exactly "real old" depending upon what it is she likes to do with her computer. If she is like most users, it is probably good enough already. I can understand wanting to update, but what is the main goal? If the current computer suffices well then I don't think a speed upgrade is a huge concern. Are you going for smaller design? Quieter operation? Less power consumption? Help us help you.
Ask your wife what she wants to be different the most. If her current computer is in some big full size ATX case, that's probably something she would like to be different. For the women folk, I usually like to stick with tiny desktop cases that are thin and sleek. This means usually going with a mATX or smaller motherboard. I like the looks of a case like this: http://www.newegg.com/Product/Product.aspx?Item=N82E168...
Then build your components around that, keeping in mind the meager power supply and the heat limitations of a small case. The Celeron e1400 you chose would be an excellent cpu, if a bit overkill. It's very low power and will have enough oomph to last years of photo editing and web surfing. As for a mATX board, I would recommend this Foxconn board http://www.newegg.com/Product/Product.aspx?Item=N82E168...
It is based and the stable G31 chipset and offers ample compatibility for upgrades. Also, foxconn is usually pretty good about getting Standby to function properly, which is something you might want. Lastly the G31 chipset does not run as hot as Nvidia's 7050 chip, meaning you can get away with passive cooling. If your wife does some gaming like the Sims however, then the Nvidia 7050 chipset may be a better option, just make sure to add a little fan onto the northbridge. A 5volt modded fan will be very quiet and keep the chipset running cool.
Finish off the build with a GB or 2 of ram (depending on the OS you want), add in wifi card and a cordless keyboard and mouse of your choosing, and finally finish off with an elegant LCD monitor.
But ya, the Celeron E1400 is a decent buy for an Intel build of this nature. I would also suggest looking at the Sempron single core lineup. The cheapest one at newegg runs at 2.2GHz, 512kb l2 cache, and cost only $30. It would be barely faster than her current 3.0GHz P4, but definitely not a down grade.
What's nice about these Semprons is that they work with RMclock to undervolt/underclock them for tremendous power savings. I use a Semrpon LE-1100 CPU in my HTPC that idles 800MHz/0.8volt with total system power consumption of only 45 watts. It loads to 2.0GHz/1.1volt with 64 watts power consumption. That's with a PVR-250 caputre card on board. My last HTPC system with a Celeron 420 took 10 more watts at idle and load, due to the fact that I could not manually adjust it's vcore or multiplier. The Celeron E1400 does have speedstep, so RMclock will work with it, but the range of vcore is unfortunately locked to only a few choices, and you'll never be able to undervolt it enough to equal the idle power consumption of the AMDs at 800MHz/0.8volt (the lowest they can possibly go). An athlon X2 is not a bad choice either, but unfortunetly RMclock does not play nice with the 65nm brisbane series and causes instability, and leaving the X2 alone using cool N quiet only generates too much heat and wastes electricity compared to the Celeron E1400.
^^The e5200 is a somewhat low cost CPU, don't get me wrong on that, but a good overclocking P45 board will run you into the $100 mark. That's a significant chunk of budget for something to be a "cheap" built.
Now, I remember when the Core 2 Duo first launched in July 2006. The slowest Core 2 Duo, the E6300 with 1.86GHz, 1066MHz fsb, and only 2MB of shared cache memory, outperformed the Pentium Extreme editition 965EE, a 3.73GHz dual core Pentium D-based chip with hyperthreading enabled, in a fair amount of applications. The 2.13GHz E6400, also with only 2MB L2 cache, put all of Intel's prior CPUs to shame, and even was able to beat out AMD's mighty FX-60 2.6GHz dual core CPU, the fastest CPU at that time. Now, you are recommending the E5200, a 2.5GHz Core-2 based CPU with 2MB l2 cache, something faster than either the e6300 or e6400. I would think stating that the E5200 is an upgrade over the P4 3.0GHz is a huge understatement. It dominates anything ever created on a Netburst architecture, even every dual core Pentium D, to such a significant degree that it is almost comical. Yes, the E5200 is an "upgrade", but if a 3.0GHz P4 was doing the job fine this whole time, putting in the E5200 would be like using a shotgun to kill a fly. And that's not even overclocked! It is a great CPU, and if it fits in the budget okay, then all the better; just try to keep in mind how powerful every CPU today has become since the old P4. Heck, the Celeron 430 sinlge core running at 1.8GHz is actually a touch faster that a 3.0GHz P4, usually being equivalent to a 3.2GHz P4. The Celeron E1400 the OP came up with is pretty much equivalent with a 3.2GHz Pentium D, and given Intel's current pricing, is probably the most logical upgrade currently over that P4.
And finally, if a single core works now, another single core will continue to work. It won't get any slower than what she currently has. Yes, dual cores are so cheap now that they can probably be recommended for anything at any budget, but sometimes the intended usage of the computer is so menial that it boils down to having a dual core for the sake of having a dual core. That's just wasted cash then, even if it is only $10 more.
I believe we can agree to disagree on this topic. After all the term "budget" is highly subjective. To each his own. I mean no offense mildliner86. Hope you have a good day.