In this study, the possibilities of noise tailoring in filamentary resistive switching memory devices are investigated. To this end, the resistance and frequency scaling of the low-frequency 1/f-type noise properties are studied in representative mainstream material systems. It is shown that the overall noise floor is tailorable by the proper material choice, as demonstrated by the order-of-magnitude smaller noise levels in Ta2O5 and Nb2O5 transition-metal oxide memristors compared to Ag-based devices. Furthermore, the variation of the resistance states allows orders-of-magnitude tuning of the relative noise level in all of these material systems. This behavior is analyzed in the framework of a point-contact noise model highlighting the possibility for the disorder-induced suppression of the noise contribution arising from remote fluctuators. These findings promote the design of multipurpose resistive switching units, which can simultaneously serve as analog-tunable memory elements and tunable noise sources in probabilistic computing machines.