Especial thanks to Alejandro M for much excellent content in this area.
Microphones are often indicated, even when amplification is not; and if you're playing ensemble with electric guitars or any other instruments with might, you are going to need some more. Tremolo can be interesting in these things. Here are some items.
One very preferable microphone for live use, is the Shure SD545. This is a dynamic mic, not a condenser. For live work condensers can be quite problematical because of the generality of their pickup, and the tone delivery is excellent for tremolo applications too. Also, the folks running sound are very likely to be familiar with dynamic mics and Shure in particular, which will help the end result a lot. Listeners seem to like it, and Shure does not build fragile. And last but not least, the silent on/off switch is very helpful when we must control it ourselves.
On a very loud stage, you may want to try a Sennheiser e609 Silver. This is a near-field hypercardioid mic, also dynamic, designed to mike guitar amplifiers. It easily handles the loudest volumes you can produce on your instruments, and faithfully transmits the tones.
If recording alone is the need, a good wide-field omnidirectional will be great, because you won't have to worry about trying not to move around or anything other than music, once the rig is good. But omnis are almost all of the "condenser" variety (I am told that the proper word is "electret", but in sales literature it's usually "condenser"), which means you can't just use a simple two-conductor wire from mike to recorder. Any given condenser mike is designed to require its own particular type of power injection into its transmission wire. Stage mikes use "phantom power" from the mixer board or DI box or other equipment, and many others, including the vast majority of the small clip-on mikes, use batteries inside them, or small battery packs, or AC adapters. "Bias power" is one type of power needed by condenser mikes when phantom power is not, and there are others. There is also, I believe, at least one other large category of power injection used for very long cable runs. The gist of it is, getting it right can be interesting.
If you can do a wide-field omni made to pick up a large area, I would do that for recording, because once it's set up you don't have to worry about anything except maybe shoe noise on the floor. But obviously it can get interesting to do omni. If it's too much, I would set up a small amplification rig as below, so you can control your electronic output by ear, and record using a good dynamic mic pointed at the speaker.
There are certainly many ways to go with this.
If the overall stage volume level is very high, you will probably need a powerful amplifier near you, perhaps a guitar or keyboard amp or baby PA or powered monitor, so that you can hear yourself. And if you like the tone your mike delivers from your instruments to a flat-response amplifier, you're done.
But there is a lot of variation in taste of timbre, especially post-amplification. Some want the quasi-overdriven tone characteristic of many Blues Band players; some desperately want to avoid that! For that sort-of-overdriven timbre you'll have to consult one or more of the other web sites out there ☺ But at least two tremolo players have reported to The Tremolo that they like a vocal-friendly range, and this can be accomplished either by appropriate mic as above, or by using a little amplifier of appropriate kind with a dynamic mic towards the PA, or both. When the stage volume is high, timbre cannot matter quite so much, because nobody including you, is going to hear your mids and lows very much!