Looking for a budget entry level HD video camera

A cold show is enough
Just an audio input is enough.

What I need is to connect a shotgun mic on top of the camera and capture the audio in the camera instead of the build-in mic

was limiting. Most "entry level" camcorders with a mic jack don't have any shoe at all.

You can either add an accessory shoe with a camera bracket

http://www.bhphotovideo.com/c/product/918053-REG/vello_cb_510_dual_shoe_brackt.html
I like these because there are two accessory shoes - one for a mic and one for a video light... plus the "angle allows steadier two-handed hand-held (even though you should not use an video camera handheld if you want steady video capture). There is a tripod screw mount in the bottom of the bracket's screw-mount, so you don't lose tripod connectivity...

or

a single mount bracket
http://www.bhphotovideo.com/c/product/743055-REG/vello__cb_600_straight_flash_bracket.html

or (I don't recommend this, but the response would be incomplete without it) you can stick them on
http://www.bhphotovideo.com/c/product/613979-REG/Impact_9031540_Adhesive_Backed_Accessory_Shoe_2_Pack.html

Since we don't know what you'll be capturing, we don't know if a mono-shotgun mic or a stereo mic (like those built-in to most camcorders) is going to be used. In either case, use of any mic built-in or external) will have problems with audio the is VERY LOUD or very soft when the mic is attached to the camcorder and there is not manual audio control. But I hope these accessory shoe solutions help.

The Canon HF R series are entry level and I *think* all have a 1/8" (3.5mm) stereo audio input. Their manual audio gain control is limited to "normal" or "attenuator" (for loud audio levels) selections in the options menu. Similarly priced camcorders from Sony and Panasonic may not have the mic jack (a couple do) and all in the same price range will have similar (poor) low light behavior due to small lens diameter and small single imaging chip.

Let us know what direction you go and what you get... and how it all works.

One suggestion: Once you pick a camcorder, DON'T buy it - but go to the camcorder manufacturer's web site, download the manual and be sure the camcorder does what you want. Discovering it does not do what you want after you buy is a hassle and can get expensive.

Heads up on most of the currently available consumer camcorders... they record AVCHD-compressed MTS files. We don't know if you plan to edit, so we don't know if your computer (hardware, operating system, video editor and supporting utility applications) can deal with that video file type - and the "tools" the camcorder manufacturers include are useless, at best.