Nuclear medicine staff is primarily exposed to their fingers during radionuclide manipulation. About 20% of these workers have risk to exceed the hand dose limit. Therefore, monitoring with ring dosimeters in terms of Hp(0.07) is advised. Most ring dosimeters make use of lithium fluoride (LiF) thermoluminescent detectors (TLDs). Different types of LiF TLDs exist, each with their advantages and disadvantages. The goal of this work was to evaluate the performance of three different LiF TLD types (MCP-N, MTS-N and MCP-Ns) for ring dosimetry during manipulation of the more novel radionuclides Lu-177, Ga-68 and I-131 within radionuclide imaging and therapy, and to provide recommendations for the most accurate dosimetric follow-up of the dose to the hands. This was done by combining measurements with TLDs and theoretical modelling of the TLD responses using Monte Carlo radiation transport simulations and microdosimetric modelling of the TLD relative luminescence efficiency. It was concluded that MTS-N TLDs are best suited for measuring doses from Lu-177 and I-131 if more than 1 mm polycarbonate equivalent shielding is provided. However, MCP-N TLDs have less than 20% under-response and are thus also acceptable in case high sensitivity is important. MCP-Ns TLDs were found to be best suited for measuring doses from Ga-68, and from Lu-177 and I-131 if less than 1 mm polycarbonate equivalent shielding is provided. The recommended TLD type strongly depends on both the manipulated radionuclide and the amount of shielding between the radionuclides and the fingers (syringe thickness and potential additional shielding around the syringe). But the approach presented here for the theoretical modelling of the Hp(0.07) response can easily be applied to select the most appropriate TLD type for other radionuclides or other amounts of shielding.