Toshiba and probably most other laptops from around that time had non-reflective 4:3 screens, but the industry switched quite quickly to PCs with glossy 16:9 widescreens. That might have had something to do with changes in the TV industry, where sales of widescreen LCD TVs were booming. Also, the PC market was still expanding beyond business users and targeting consumers who wanted to watch DVDs on their laptops. Either way, the cost of widescreen LCDs kept falling as manufacturing volumes went up, and now 4:3 screens have almost completely disappeared.
The good news is that you can still get that sort of laptop from Fujitsu and perhaps other business-oriented suppliers. The bad news is that these machines are harder to find and usually more expensive than mass market laptops from HP, Dell, Lenovo, Acer, Asus and Samsung.
But there are two issues to consider. The first is the physical size of the screen, where bigger is usually better … unless you have to lug it around. The second is the screen resolution, which is the number of pixels (picture elements) on the screen. If the screen size stays the same, then increasing the resolution will make text and images smaller. If the resolution stays the same, then increasing the screen size will make text and images bigger. You need to decide whether you actually need bigger characters, or more lines of characters. For example, is it important to see 38 lines of a spreadsheet on screen at once, rather than 32, or whatever?
You are correct in noting that you will need a much bigger widescreen to get the same physical depth as you have today. However, if you buy a laptop with a standard widescreen, you probably will not lose any resolution. Laptops like your Toshiba typically ran Microsoft Windows XP with a 4:3 screen resolution of 1024 x 768 pixels, which is known as XGA (eXtended Graphics Array). Today’s standard resolution is 1366 x 768 (WXGA) on a 16:9 widescreen laptop, so the vertical resolution is exactly the same. You will get the same number of lines of text in a word processor and rows in a spreadsheet, though the text may be slightly smaller, depending on the size of the screen.
Since you have a 14.1in screen at the moment, I would expect a laptop that shows 1366 x 768 pixels a 15.6in screen to be an acceptable compromise. This is currently the most common option, and generally the best value for money. Also, Windows 7 lets you make text bigger. (The options under “Make text and other screen items larger or smaller” are “Medium 125%” and “Larger 150%”.)
Of course, you can now buy laptops with even more vertical resolution. If that appeals, look for something with a screen resolution of 1440 x 900 (WXGA+), which is a 16:10 ratio, or 1920 x 1080 (Full HD). These resolutions are more common on 17in screens, which means wrestling with a much bigger, bulkier machine.
You will usually pay extra for a laptop with a 17.3in screen, but prices have come down a lot since you bought your Toshiba. For example, you can buy a Lenovo G770 laptop with a 17.3in 1600 x 900 widescreen for £469.99 from Amazon.co.uk, which compares with £399.97 for the Lenovo G570 version with a 15.6in 1366 x 768 widescreen.
My son uses a higher-spec Lenovo with a 17.3in screen, so I can confirm that the screen is not unbearably shiny and that the keyboard is above average quality. However, you should look at some 17.3in laptops in a shop to make sure you are happy with the size of text on the screen.
If you really want something closer to what you have now, one option is the Fujitsu Lifebook P701, which has a 12.1in WXGA (1280 x 800) anti-glare screen. However, this is sold as a business ultraportable and, like old IBM X series, lacks a DVD drive. A P701 with an Intel Core i3-2310M processor and 2GB of memory costs £501.85 from Amazon.co.uk (£306.69 off), though I notice the blurb fails to mention the screen resolution. Searching for P701XMF011GB will find other sources.
It seems to me that you would be paying more and losing out in other areas for the sake of 32 extra pixels when compared with a mainstream 1366 x 768 widescreen laptop.