reporting results of a multivariate logistic regression using the glm function in R

I would like to use the glm() function in R to run a multivariate logistic regression. I have also run bi-variate statistics for each variable but want a test that controls for all variables at once (what I understand the glm function in R does – let me know if I should use a different function). My problem is that I don’t know what to report in an academic paper and can’t find anything online. There are clear guidelines for reporting other tests (example: t (34.17) = 2.22, p = 0.033) but I don’t know what to report for the glm. Here is the output of my glm:

Call:
glm(formula = EPI ~ premed + kg + sim + bup + premed.min + ami.type + breed, family = "binomial", data = df)

Deviance Residuals: 
    Min       1Q   Median       3Q      Max  
-0.7316  -0.2980  -0.2351  -0.1573   2.9108  

Coefficients:
                    Estimate Std. Error z value Pr(>|z|)  
(Intercept)        -1.364678   1.239446  -1.101   0.2709  
premedT             1.103479   0.499234   2.210   0.0271 *
kg                 -0.032467   0.014633  -2.219   0.0265 *
simS                0.193276   0.431850   0.448   0.6545  
bupN                0.037000   1.048603   0.035   0.9719  
premed.min          0.002211   0.002542   0.870   0.3845  
ami.typeCRI       -12.604613 781.507743  -0.016   0.9871  
ami.typeDRIP       -0.226335   0.466006  -0.486   0.6272  
breedYorkshireMix  -0.852239   0.489624  -1.741   0.0818 .
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

(Dispersion parameter for binomial family taken to be 1)

    Null deviance: 272.44  on 938  degrees of freedom
Residual deviance: 255.21  on 930  degrees of freedom
  (1 observation deleted due to missingness)
AIC: 273.21

Number of Fisher Scoring iterations: 15

It doesn’t help that I cant figure out how I would report a bi-variate logistic regression either (I’ve seen people report odds ratios, χ2 values etc). I have found out how to get confidence intervals and odds ratios in R if I need those:

> exp(cbind(OR = coef(LM), confint(LM)))
Waiting for profiling to be done...
                            OR         2.5 %       97.5 %
(Intercept)       2.554629e-01  2.222514e-02 2.873313e+00
premedT           3.014635e+00  1.198440e+00 8.735251e+00
kg                9.680544e-01  9.402870e-01 9.957784e-01
simS              1.213217e+00  5.144926e-01 2.832683e+00
bupN              1.037693e+00  5.650816e-02 5.366901e+00
premed.min        1.002213e+00  9.966528e-01 1.006788e+00
ami.typeCRI       3.356495e-06 9.742338e-102 1.000098e+12
ami.typeDRIP      7.974511e-01  3.090303e-01 1.957706e+00
breedYorkshireMix 4.264589e-01  1.724568e-01 1.213685e+00
There were 36 warnings (use warnings() to see them)
> warnings()
Warning messages:
1: glm.fit: fitted probabilities numerically 0 or 1 occurred

I want to say something like "The results of the multivariate logistic regression indicated that subjects given pre-medication "T" were more likely to have outcome "EPI" than subjects given pre-medication "X" (blah, blah, p = 0.027) and subjects that had lower "kg" were also more likely to have outcome "EPI" than subjects that had higher "kg" (blah, blah, p = 0.0265)."

EDIT: EPI is a binary variable that is assigned 0 or 1