Which Bootstrap method is most preferred? Maybe this question depends on the given data, but is there a "better" bootstrap method than the others?  I'm simply using a one variable dataset (that consists of the differences between football scores (2 teams) over the past 15 weeks)..
First note the right skew of this data, I feel like this will take into consideration which bootstrap I would recommend as being "better" or most accurate for the representation of the data.

First here is the standard bootstrap interval
N <- 10^4
n <- length(Differences)
Differences.mean <- numeric(N)
for(i in 1:N)
{
x <- sample(Differences, n, replace = TRUE)
Differences.mean[i]<- mean(x)
}

lower = mean(Differences.mean)-1.96*sd(Differences.mean) #Lower CI
upper = mean(Differences.mean)+1.96*sd(Differences.mean) #Upper CI
= (8.875, 10.916)

 mean(Differences.mean)-m  #The bias is fairly small also
= -.0019

Here is a bootstrap percentile interval
 quantile(Differences.mean,c(.025,.975)
 = (8.893, 10.938) 

Lastly here is the Bootstrap T interval
Tstar = numeric(N)
for(i in 1:N)
{
y =sample(Differences, size = n, replace = TRUE)
Tstar[i] = (mean(y)-m) / (sd(y)/sqrt(n))
}
q1 = quantile(Tstar,.025) #empirical quantiles for bootstrap t (lower)
q2 = quantile(Tstar,.975) #empirical quantiles for bootstrap t (upper)

mean(Differences)-(q2*sd(Differences/sqrt(n)))
mean(Differences)-(q1*sd(Differences/sqrt(n)))
= (8.925, 10.997)

In addition even the t confidence interval seems pretty accurate
 t.test(Differences, conf.level = .95, alternative = "two.sided")
 = (8.867, 10.928)

My conclusion would be to choose the bootstrap t interval because it reflects the right skew of the data, it is stretched further to the right than any of the others. My sample size is 224. I think sample size plays a huge role in my conclusion, but my initial question was "is there a better bootstrap method than the others?".. Maybe it really does depend on the data and sample size. Hopefully this isn't too broad.
 A: It's never too late to fix an error... At least I think there is an error in the implementation of the bootstrap $t$ interval, which requires a bootstrap within the bootstrap (double bootstrap).
Note: I refactor the R code for clarity. And since the OP didn't provide data or the code to reproduce the data, I use the nerve data from the book All of Nonparametric Statistics by L. Wasserman. The measurements are 799 waiting times between successive pulses along a nerve fiber and was originally reported in Cox and Lewis (1966).
The goal is to compute the studentized bootstrap interval defined as:
$$
\begin{aligned}
\left(
T - t^*_{1-\alpha/2}\widehat{\operatorname{se}}_{\text{boot}},
T - t^*_{\alpha/2}\widehat{\operatorname{se}}_{\text{boot}}
\right)
\end{aligned}
$$
where

*

*$T$ is the statistic of interest (here skewness);

*$\widehat{\operatorname{se}}_{\text{boot}}$ is the standard error of the bootstrapped statistics $\tilde{T}_1, \ldots, \tilde{T}_B$;

*$t^*_q$ is the $q$ sample quantile of $T^*_1, \ldots, T^*_B$; and

*$T^*_b$ is the bootstrapped pivotal quantity:
$$
\begin{aligned}
T^*_b = \frac{\tilde{T}_b - T}{\widehat{\operatorname{se}}^*_b}
\end{aligned}
$$
The standard error $\widehat{\operatorname{se}}^*_b$ of $T^*_b$ is estimated with an inner bootstrap inside each bootstrap iteration $b$. That's computationally expensive.
set.seed(1234)

# Dataset used in the book All of Nonparametric Statistics by L. Wasserman.
# https://www.stat.cmu.edu/~larry/all-of-nonpar/data.html
x <- scan("nerve.dat")
n <- length(x)

The bootstrap is a general procedure, so let's make the implementation general as well by defining a function estimator to calculate a statistic $T$ (for the nerve data it's the skewness) from a sample $x$ as well as a function simulator to generate bootstrap resamples of $x$.
estimator <- function(x) {
  # sample skewness
  mean((x - mean(x))^3) / sd(x)^3
}
simulator <- function(x) {
  sample(x, size = length(x), replace = TRUE)
}

So here is the bootstrap $t$ implementation outlined in the question. I've highlighted the errors in comments.
alpha <- 0.05
B <- 2000

# Warning: This code snippet doesn't implement the bootstrap t correctly.
Tstat <- estimator(x)
Tboot <- numeric(B)
Tstar <- numeric(B)

for (i in seq(B)) {
  boot <- simulator(x)
  Tboot[i] <- estimator(boot)
  # > Error: Doesn't bootstrap the std. error of Tboot[i] correctly.
  Tstar[i] <- (Tboot[i] - Tstat) / sd(boot)
}

q.lower <- quantile(Tstar, alpha / 2)
q.upper <- quantile(Tstar, 1 - alpha / 2)

# > Error: Uses the standard deviation of the sample x
#    instead of the standard error of the statistics T
c(
  Tstat - q.upper * sd(x),
  Tstat - q.lower * sd(x)
)
#>    97.5%     2.5% 
#> 1.451426 2.102211

And here is the correct way to do the bootstrap $t$ method. Note that this procedure requires to do bootstrap inside the bootstrap. This is more computationally intensive but (we expect) more accurate.
Tstat <- estimator(x)
Tboot <- numeric(B)
Tstar <- numeric(B)

for (i in seq(B)) {
  boot <- simulator(x)
  Tboot[i] <- estimator(boot)
  # > Bootstrap the bootstrap sample to estimate the std. error of Tboot.
  boot_of_boot <- replicate(B, estimator(simulator(boot)))
  Tstar[i] <- (Tboot[i] - Tstat) / sd(boot_of_boot)
}

q.lower <- quantile(Tstar, alpha / 2)
q.upper <- quantile(Tstar, 1 - alpha / 2)

# > Use the bootstrap estimate of the std. error of T.
c(
  Tstat - q.upper * sd(Tboot),
  Tstat - q.lower * sd(Tboot)
)
#>    97.5%     2.5% 
#> 1.463658 2.292374

Example 3.17 of All of Nonparametric Statistics reports the studentized 95% interval for the skewness of the nerve data as (1.45, 2.28). This agrees well with the result obtain with the second/correct implementation of the bootstrap $t$ above.

References
L. Wasserman (2007). All of Nonparametric Statistics. Springer. 
Cox, D. and Lewis, P. (1966). The Statistical Analysis of Series of Events. Chapman and Hall. 
Nerve dataset downloaded from https://www.stat.cmu.edu/~larry/all-of-nonpar/data.html 
A: As Michael Chernick notes, it would be useful to also look at the bias-corrected (BC) and bias-corrected and accelerated (BCa) bootstrap.
The BCa variant in particular attempts to deal with skewness in data, as you apparently have. DiCiccio & Efron (1996, Statistical Science) found that it performs well, as do Davison & Hinkley, Bootstrap Methods and their Applications (1997).
Why does my bootstrap interval have terrible coverage? is related, and I would especially recommend the article by Canto et al. (2006) that I cite there. And in the end, I agree that the answer is likely related to sample size, as well as your underlying distribution, and the pivotality or non of the statistic you are bootstrapping.
