Ultimately depends how much (or little) you want to spend vs. function and quality.
Moto G and Moto E have good reputations.
1st Gen Moto G (4.5 inch screen) is being replaced by 2nd Gen (5 inch screen). You can still pick up some really good deals on the 1st Gen 4G if that is good enough for you. I picked up one in a big Tesco's (Sutton) for £89 (even though the website STILL says £139) a couple of months ago. But the website does say you can boost Tesco points (and so, effectively, halve the cost if you've got enough points).
Same model currently available on Amazon for £105.29.
1st Gen comes with Android 4 (KitKat), but the OTA update to Android 5 (Lollipop) is now under way.
The above are SIM Free. Tesco may sell you a Tesco locked one for less (e.g. £95) and I gather can be readily unlocked with a code bought on ebay for a couple of squid - but I've never tried (so not personally recommending).
If you are prepared to splash out only a little more, you could go for the 5 inch 2nd Gen.
Moto E is a slightly "lesser" model. But 2nd Gen probably equivalent-ish to Moto G 1st Gen.
Agree with Batch. I have had a 1st generation Moto G for about a year now. It automatically upgraded to the latest Android OS, lollipop. I have been really pleased with its performance considering that it is a budget phone.
Just swap over the SIM and sd card. If you go for a 1st Gen Moto G, do make sure it is the 4G model (as the others, as well as not being 4G, do not have a microSD card slot).
BTW, it takes a microSIM (what does your old phone take?). If not the same and the SIM for the old phone does not have the pushout to convert into a microSIM, you will either need to get a SIM cutter (risky) or get Three to send you a replacement SIM to swap over with (AFAIK, all the current SIMs can be converted from standard size into micro or even nano). Not sure what Three's process for handling this sort of situation is. I know GiffGaff SIM swap is very slick process (as I've done it previously with them when I was switching from a phone with old standard size SIM to a phone with microSIM).
Can't say I've found it sluggish (but then I've never had another smart phone to compare it with). I find it is about the same as my Nexus 7 tablet.