I use wire transfers for brokerages, since most brokerages do not let you trade for a good 5 days after an ACH transferred is started. Wires are pretty much immediate.

For a savings account I don't think it matters. Most online savings banks start paying you interest as soon as you initiate the ACH transfer.

401k loans are a bad idea. Your money is taken out of the market when you have a loan against it. If you lose your job (leave, get laid off, etc) your loan becomes immediately do. If you can't pay your loan, your funds are sold and you pay penalties and taxes.

Find another source of funds - or save money separately from your 401k for the improvements you are looking to do.