I believe RMSEA < 0.08 is considered acceptable. Hu & Bentler ("Cutoff criteria for fit indexes in covariance structure analysis", 2014) recommded a cutoff = 0.06 for a "relatively good fit". They are rules of thumb, though, but generally accepted.
Root-mean-square error of approximation (RMSEA), the issues regarding the sample size, parameters which are selected for the estimates and covariance matrix of population are avoided by RMSEA. It should be 0.08 or less than that for best fitness of model (Bentler & Bonett, 1980; Hu & Bentler, 1999; Carmines & McIver, 1981).
RMR, the root mean square residual, is an index of the amount by which the estimated (by your model) variances and co variances differ from the observed variances and covariance. Smaller is better (Karl L. Wuensch, 2013). UCDHSC Center for Nursing Research (2006), verified that with RMR = 0 indicating a perfect fit.