How to fit multiple average (horizontal) lines in ggplot in R

I want to fit multiple horizontal lines to a plot, where each line represents the mean of a different category in my data.

lets say I have the following data frame

product <- c("A","A","B","B", "A","A", "B","B", "C","C", "D", "D", "C","C", "D", "D")
measurement <- c(120, 122, 42, 44, 119, 118, 45, 43, 280, 281, 502, 501, 279,278, 503, 504)
sample_data <- data.frame(product, measurement)

I would like to create a result as following

ggplot(sample_data, aes(x=seq(length(sample_data$measurement)), y=measurement, colour= product)) +
  geom_point() +
  labs(x = "Data Points") +
  geom_smooth(aes(group= product), formula = y~1, method="lm", col="blue", se=TRUE, size=.005)

I have two questions:

How can I make sure that each line represents the mean of each product?
How can I show the value of each mean line over the line or somewhere in the legend?

Any help would me much appreciated.

Solution

If you want to do it all "inside" ggplot, you could do:

library(geomtextpath)

ggplot(within(sample_data, `Data Points` <- seq(nrow(sample_data))),
       aes(x = `Data Points`, y = measurement, colour = product)) +
  geom_point() +
  geom_textsegment(aes(y = ave(measurement, product), 
                   x = ave(`Data Points`, product, FUN = min),
                   yend = ave(measurement, product),
                   xend = ave(`Data Points`, product, FUN = max), 
                   label = after_stat(y)), 
                   vjust = -0.2, textcolour = "black", linetype = 2)