Playing mono records properly without breaking the bank - a phono pre-amp question.

I play a lot of Mono Jazz LP's from the late 40's early 50's.

Most cartridges will play Stereo and Mono well. For your described use, TT with Stereo cartridge is all you need. 

Last night I listened to mostly Mono Jazz LPs for 3 hrs with an audiophile friend. They all sounded quite involving (you will find, stereo or mono, it depends on the recording engineer's skills as much as the artists).

I moved my McIntosh MODE switch to Mono, back to Stereo, both sound very good, some might be slightly better in Mono mode, but Mono played by Stereo cartridge is still quite involving.

LP Stereo playback began in 1958. Some engineers anticipated that and recorded with two or more mics to be ready. Those masters can be re-engineered to Stereo successfully. Avoid 'mono reprocessed to stereo', they generally sound worse than the mono original.
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I do advise that you get a TT with the possibility of adjustments.

I use this fully adjustable TT  which fits your budget

https://www.amazon.com/Audio-Technica-AT-LP120XUSB-Direct-Drive-Hi-Fidelity-Anti-Skate/dp/B07N3S4X3P/ref=asc_df_B07N3S4X3P/?tag=hyprod-20&linkCode=df0&hvadid=312150547590&hvpos=1o2&hvnetw=g&hvrand=8381325411824345964&hvpone=&hvptwo=&hvqmt=&hvdev=c&hvdvcmdl=&hvlocint=&hvlocphy=9003512&hvtargid=pla-681677883325&psc=1&tag=&ref=&adgrpid=70581793108&hvpone=&hvptwo=&hvadid=312150547590&hvpos=1o2&hvnetw=g&hvrand=8381325411824345964&hvqmt=&hvdev=c&hvdvcmdl=&hvlocint=&hvlocphy=9003512&hvtargid=pla-681677883325

The supplied cartridge is factory aligned, just level the TT and off you go. You may never change anything, but, then again, you might.

I changed the cartridge to this one (so I could lower the tracking weight). 

https://hifiheaven.net/shop/Shure-M97xE-Audiophile-Phono-Cartridge?language=en&currency=USD&gclid=Cj0KCQiA_rfvBRCPARIsANlV66MTfCEX1XGRPd6RY8AFCDxTaPR1TXzZgw3rNCawEV6Nlr320_5Wfw4aAs4iEALw_wcB
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McIntosh MODE Switch has a MONO mode. (some, not all models).  

Stereo; Mono; Reverse Stereo; L or R hither and thither separately or together.

Mode Switch is a great help when balancing your system. Stereo Reverse is very revealing of any imbalance. My speakers have two rheostats for brilliance and Presence. They need to match each other, the Mode Dial is a big help with that. IF you change a cartridge, or check your existing one, Stereo Reverse is very helpful refining anti-skating for proper l/r groove tracking. L to R, ... all help get it right, I wouldn't live without it. 

remote controlled stereo/mono switch.

add it later if desired

https://www.kabusa.com/frameset.htm?/m1200.htm

you need to go to the home page, scroll down, it's next to the last item

https://www.kabusa.com/frameset.htm?/m1200.htm

Elliott, Your experience is slightly different from mine.  I played all LPs, mono or stereo, with a stereo cartridge for the first ~35 years of my audiophilia.  And I agree with you partly, I never felt a crying need for a mono switch or a mono cartridge.  However, the recent interest in mono LPs and mono playback induced me to acquire preamplifiers with a mono switch (I have two systems) and also a mono cartridge.  Since then, using these devices, I have been impressed with the positives of playing mono LPs in mono mode (either by using a mono cartridge or by switching or both). There is less high frequency "hash", for sure, but also there is enhanced clarity and a closer approach to the live sound.  I wouldn't go without at least a preamplifier with a mono switch, these days.  For certain LPs produced in both stereo and mono during the transition phase from mono to stereo, I can even say I prefer the mono version. On the other hand, I wouldn't argue that a casual listener could not be happy in stereo.

hrabieh, optimizing mono playback can become complex, but basic enjoyment doesn't need to be.  Yes, there can be considerations for when the record was issued, groove width, even EQ.  But I believe the first consideration is which mono records will you listen to?

There are multiple reissues now of older mono LPs.  Since mono cutter heads are no longer available (so far as I know) these are cut with stereo cutter heads.  This simplifies matters as a stereo cartridge stylus should be just fine.  A mono switch may still be beneficial, such as Elliott suggested, to reduce background noise.

However, if you intend to play original monos from the late '40s to early '60s, by which time initial mono releases ended, then there may be no simple playback solution if you are concerned about sonics.  A modern stereo cartridge can be used but will not be optimized for stylus size, pickup type (no vertical groove information, only noise).  Also multiple EQs were utilized by different labels (requiring selectable settings).  So the best answer there is a second cartridge and specialized phono stage, which you want to avoid, at least to begin with.