Check Luminous landscape for discussions about lightmeters preferred by landscapists. IIRC, most of them will use a 1 degree spot-meter. The discussions are not so much about what type of meters, as compared to the advantages and disadvantages of different types of spot-meters.
For portrait work, since you did not mention ANY details, it's probably best to assume ALL possibilities and in that case, any competent meter with the ability to read both reflected and incident lights, take flash readings as well as calculate ratios, and be able to attach or have a spot or pseudo-spot function would be handy.
If you choose a flshmeter with a 1 degree spot function, you would not have to get a seperate spot-meter for landscape work.
I'm not trying to patronize, but from the way you asked, I get the impression you might not have used handheld meters before, or may not know how to meter a scene. Bear in mind - a meter only reads and measures. It's up to the photographer to do all the 'visualization' and mental calculations of what would work and what would not for a particular scenario. Knowing how light behaves, and what to meter also forms a crucial part of the process.