It's usually pretty easy to upgrade the memory, and for machines in the $400-$500 range, I tend to recommend going with full-warranty manufacturer refurbished systems from Dell or Lenovo, where you can with some hunting get higher-end business machines at that price range that tend to be much more durable than the consumer machines that sell new (you may still need to put 4gb more to get to 8gb at that price.)

Dell is almost constantly running some sale or another via their outlet, which makes them very convient; I tend to prefer Lenovos for the newest generation of machines, but the Dells aren't bad and at 15-30% off the base refurb price they are very hard to say no to. https://twitter.com/DellOutlet is the best place to watch for sales.

For example, right now they've got:
Day 1 - Latitude 5000, 6000, or 7000 Series and Monitors
Save 25% on any Dell Outlet Business Latitude 5000, 6000, or 7000 Series Laptop or Monitor with coupon* code below!
Limited time, while supplies last.

Coupon code:
3ZFRNJ5M7X3DSN

The Latitudes E6420 and E6430 are a bit chunky (and a good bit heavier than the competing Lenovo T420/T430), but otherwise very nice machines, and the E6430u and E7440 are both very nice business light weight 14" machines; there are some of each for about $525-550 after discount still available.

Although the inventory is looking a mite picked over... the Latitude 3000 series coupon (which is their lower end business line, replacing what used to be Vostro) coming up for later in the week might be particularly intriguing.

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What processor do you have? If it was a reasonably high-end one for 4-5 years ago, you might do better upgrading the RAM and SSD.

If it's a low-end one, you will probably want to upgrade.

As a rule of thumb to boil down what I said up-thread, anything i5 or i7 should still be good enough for almost anyone (and many, although not all, i3 chips will be good enough for most people, especially since there weren't any ultralight ones yet using i3s back at the beginning of 2010 when they came out.)

Most "Core 2 Duo" chips -- except some of those in ultralight machines -- will be good enough for most people, although there is a very big difference in how happy I'd be with the most basic ones I'd recommend (say, the T7200 or L9400, which are between them the two slowest machines I'd be willing to use today) and something high-end (say, a P9700 which would be a machine I'd still be happy to use today and is faster for some things than some ultrabooks sold new.)

For anything else older (Pentium Dual Core, Celeron, Atom) if it's as old as 2009-2010, it's time to upgrade, and indeed, probably worth shooting a little higher end if you think you may keep this next system longer than a couple or maybe 3 years.

(One other thing to consider is battery life; for some folks, this doesn't matter at all, but for those of us who use the machines heavily on battery, often by the three year mark -- if not much sooner -- if we're not rotating batteries while new, the battery will need replacing anyway. At the low end of the market, a manufacturer-branded replacement batter can be something like 1/3 the cost of the original machine!)