Best I can suggest is the cheapest handheld type K readout you can buy, together with the best handheld probe you can get your hands on.
It's worth doing some research on the probes and deciding exactly what you want to do with them. The thermocouple is where the money is most usefully spent. Even the cheapest handheld readouts are likely to be at least as accurate as the best thermocouple you can reasonably buy.
Once you know what you want to do, it's also worth picking up the phone and talking to Omega and getting their recommendation.
I think the ones I have bought from them have been KHXL handled probes (but bear in mind I may not have had exactly the same needs as you).
http://www.omega.com/ppt/pptsc.asp?ref=KHXL_NHXL&Nav=tema06
I think I settled on KHXL-14G-RSC-24, the 24" long version.
I also chose a grounded junction for faster response (but this may not be such a good idea if you are likely to be subjecting it to big, fast temperature changes; an insulated junction might be better).
The reasons for the various choices;
K to work with a wide selection of portable instruments. Special limit materials give higher accuracy.
HXL for the 1335 degC short-term temperature rating on the sheath material; it is just getting into the forge-welding temperature range.
14; 1/4" diameter is rigid enough to hold it wherever I want to measure. G; grounded junction for fastest response, means I don't have to hold it very long wherever I want to measure. As I say, YMMV.
I went 24" long to allow me to measure at the back of the forge without burning my hands or melting the handle.
It looks like a miniature type K plug on the assembly in the link, but it is worth checking on the phone as I can't see it specified. Most portable instruments use "miniature" plug/socket connections, which use flat pins.
I use "TM902C" handheld readouts, bought off ebay for under 4 GBP (around $6) delivered. They only read degC, but read to 1365 degC (2489 degF), agree with my more expensive instruments, plus the calibrator at work, and are cheap enough that I won't worry if/when I break them. Some of the TM902Cs I have say -50-1300 degC on the front, but actually read to 1365 degC. I also have one that says -50-750 degC on the front but this also reads to 1365 degC.
IR measurement for forges is difficult. There are just too many variables. Emissivity is affected by temperature and by scale. IR from the flame, either direct or reflected, also causes errors. I gave up on my 1600 degC (2912 degF) IR instrument and lent it to a smith a year or so ago. I'd forgotten until now.